Since we were talking about the meaning of the Hebrew term translated here "messiah" in the NWT (ONLY here, as elsewhere it is always translated "anointed") and some other Christian translations, it is worthy to note that the earliest Christian interpretation of the term in this passage understood that it had reference to the priests of the Temple (this partially preserves the original sacerdotal understanding of the oracle, attested in such writings as the Testament of Levi).
"Having mentioned therefore seventy weeks, and having divided them into two parts, in order that what was spoken by him to the prophet might be better understood, he proceeds thus, 'Until khristos the prince there shall be seven weeks,' which make forty-nine years. It was in the twenty-first year that Daniel saw these things in Babylon. Hence, the forty-nine years added to the twenty-one, make up the seventy years, of which the blessed Jeremiah said that the sanctuary shall be desolate seventy years from the captivity that befell them under Nebuchadnezzar, and after these things the people will return, and sacrifice and offering will be presented, when khristos is their prince. Now what khristos does he mean but Jesus son of Josedek, who then returned with the people and in the 70th year upon the rebuilding of the temple offered sacrifices according to the Law? For all kings and priests are called khristoi" (Hippolytus, On Daniel 2.13-14).
"At that time, 'an anointed one, a ruler', prophesied by Daniel, came to an end. For up to Herod, there were 'anointed ones, princes'. These were the high priests, who presided over the Jewish people, beginning with the restoration of the temple during the reign of Darius in the 65th Olympiad, and lasting to Hyrcanus in the 186th Olympiad [i.e. 36-33 BC]" (Eusebius, Chronici Canones 373-374).
Now what is found in the immediate context? The precedent for the term mshych "anointed one" in v. 25-26 is found in the preceding verse: "Seventy weeks are determined for your people and for your holy city, to finish transgression, to bring sins of completion and to expiate iniquity, to seal vision and to anoint the Holy of Holies". The OT has many references of anointing the altar and the Holy of Holies in the tabernacle and Temple: "Purify the altar by making atonement for it, and anoint it to consecrate it" (Exodus 29:36), "Use the oil to anoint the Tent of Meeting, the ark of testimony, the table and all its articles, the lampstand and its accessories, the altar of incense, the altar of burnt offering ... you shall consecrate them so they will be most holy" (Exodus 30:26-29), "take the anointing oil and anoint the tabernacle and everything in it, consecrate it and all its furnishings and it will be holy" (Exodus 40:9), "Moses took the chrism and anointed the tabernacle and everything in it to consecrate them, he sprinkled the altar seven times and anointed the altar" (Leviticus 8:10-11), "on the day Moses finished setting up the tabernacle he anointed and consecrated it" (Numbers 7:1), etc. Only the high priest could anoint the Holy of Holies and priests were referred to as "anointed" (mshych, khristos) in the relevant literature (see, for instance, Leviticus 4:3, 2 Maccabees 1:10). See also Zechariah 4:14 which refers to Joshua son of Jozadak, the first high priest after the Exile, and Zerubbabel as the "sons of oil". The high priests were also referred to as ngyd "ruler" (= ngyd mshych "anointed ruler" in Daniel 9:25) in Jeremiah 20:1, Nehemiah 11:11 ("ruler of the House of God"), 2 Chronicles 31:10, 13, and most importantly, Daniel 11:22 ("the ruler of the covenant") whose destruction at the hands of Antiochus Epiphanes related in that verse corresponds to the cutting off of the "anointed one" in 9:26 (compare also 1 Enoch 90:8).
The purpose and intent of ch. 9 rather comes into focus when it is understood that it is talking about the same thing that the visions in ch. 8 and 10-11 are concerned with: the sanctity of the Temple in the post-exilic period, climaxing in the defiling of the Temple under Antiochus Epiphanes (the "little horn" from the kingdom of Greece in ch. 8). The question of "how long" from ch. 8 receives a specific answer in the periodization scheme of ch. 9, and the question of "why" the Temple remains in such a state so long after the return from Exile is also answered by the angel. The scheme the author adopts is intelligible because it is interpretive of both Jeremiah and Leviticus (it uses Leviticus to interpret Jeremiah), such that the 70 years is expanded into a duration of 490 years on account of the "sevenfold" curse from Leviticus (the curse alluded to in Daniel 9:11). There is nothing about when a "Messiah" is supposed to come in the prayer that Daniel gives; he is asking for the curses against Jerusalem and its Temple to come to an end. It is the same with ch. 8, which inquires on when the defiling of the sanctuary would come to an end so that it would be reconsecrated (v. 13-14), i.e. anointed by the high priest. The interpretation in the OP, which makes the seventy weeks climax with the destruction of Jerusalem by Titus (with the Temple never being rebuilt again), is wholly contrary to the thought in v. 24 which states that the period is one in which the holy city atones for its transgression, ending with it being brought into a state of everlasting righteousness.
To lay this out in further detail, Daniel first was counting the years for the "successive devastations of Jerusalem to come to an end" (v. 2), i.e. the 70 years of Jeremiah, and the prayer referred to the former desolation of Jerusalem in v. 12, 16, 17, 18 and the destruction of the Temple in v. 17: "For your own sake, Lord, let your face smile again on your desolate sanctuary". The problem faced by the author of Daniel was (1) the fact that the glorious restoration of the Temple and Israel in Isaiah 60-62, Ezekiel 40-48, Zechariah 12-14, had not yet been realized in the Seleucid era but instead Judah remained under foreign oppression in a "time of trouble", and (2) the fact that the Temple was defiled and devastated a second time by Antiochus Epiphanes and his mysarch (cf. Daniel 11:31). As 1 Maccabees described the events in part:
"Antiochus turned about and advanced on Israel and Jerusalem in massive strength. Insolantly breaking into the sanctuary, he removed the golden altar and the lampstand for the light with all its fittings, together with the table for the loaves of offering ... the golden decorations in front of the Temple, which he stripped of everything ... leaving the places a shambles...Two years later the king sent a mysarch through the cities of Judah. He came to Jerusalem with an impressive force and addressing them with what appeared to be peaceful words, he gained their confidence; then suddenly he fell on the city dealing it a terrible blow, and destroying many of the people of Israel. He pillaged the city and set it on fire, tore down its houses and encircling wall, took the woman and children captive ... They shed innocent blood all round the sanctuary and defiled the sanctuary itself. The citizens of Jerusalem fled because of them, she became a dwelling place of strangers ... her sanctuary became as deserted as a wilderness" (1 Maccabees 1:20-24, 29-39).
The answer to this unexpected turn of events was that the 70 years of the prophet Jeremiah were not yet completed, even hundreds of years later. In the vision, the angel Gabriel expands the original 70 years into 490 years on the basis of the "curse" mentioned in Daniel's prayer: "The whole of Israel flouted your Law and turned away, unwilling to listen to your voice; and the curse and imprecation written in the Law of Moses, the servant of God, have come pouring down on us because we have sinned against him" (Daniel 9:11). The curse referred to here is the one in Leviticus:
"If you have set yourselves agaisnt me and will not listen to me, I will heap these plagues on you in sevenfold punishment for your sins... I will set myself against you in fury and punish you sevenfold for your sins... I will reduce your cities to ruin; I will lay your sanctuaries waste, I will no longer breathe the fragrance that would appease me. I will make such a desolation of the land that your enemies who come to live there will be appalled by it. And I will scatter you among the nations ... Then the land will observe its sabbaths indeed, lying desolate there, while you are in the land of your enemies ... But they must atone for their sin, for they have spurned my customs and abhorred my laws" (Leviticus 26:21, 27-34, 43).
The angel takes this warning literally and multiplies Jeremiah's 70 years by 7 (70 x 7 = 490 years), expanding the period of punishment for centuries longer during which the people are to "finish transgression, to bring sins to completion and to expiate iniquity," just as Leviticus 26:43 states that the period of punishment is for the people to "atone for their sin". Thus, even tho Jerusalem may be rebuilt and the sanctuary anointed again by the "anointed" priests, the promised punishment of God "laying your sanctuaries waste" would not be completed until the full "seventy weeks" are over and the people's sins atoned. The interpretation of the seventy weeks in Daniel 9:25-27 thus culminates in the final restoration of the Temple, not its final destruction.
The 70th week concerns the same defiling of the Temple related in ch. 8, the "little horn" of the kingdom of Greece, i.e. Antiochus Epiphanes who caused sacrifice and oblation to cease and who installed the abomination of desolation on the sanctuary: "He grew great even up to the prince of the host, from whom the perpetual sacrifice was taken away and whose sanctuary place was cast down. A host was given over together with the perpetual sacrifice" (8:11-12). Then the prophet asks: "For how long is the vision of the perpetual sacrifice and the desolating transgression, and his giving over of sanctuary and host to be trampled?", and he is told that it would last a little more than three years "until the sanctuary is reconsecrated" (8:13-14). This is parallel to 12:11 when the prophet is told that "from the time when the perpetual offering is taken away and the desolating abomination is set up is one thousand two hundred and ninety days", i.e. about 3 1/2 years. We have the same scheme in ch. 9. At the beginning of the seven-year period, the high priest would be cut off (= Daniel 11:22) and then "the host of a ruler who is to come will destroy the city and the sanctuary" and at the midpoint of the week "he will suppress sacrifice and offering for half a week (i.e. 3 1/2 years) and the desolating abomination will be in their place until the predetermined destruction is poured out on the desolator" (9:26-27). This corresponds exactly to what is said in ch. 11 with respect to Antiochus' defiling of the Temple: "Forces of his will come and profane the sanctuary citadel; they will abolish the perpetual sacrifice and install the desolating abomination there" (11:31). All these parallels within Daniel show that the person who ends sacrifice and offering is not a messianic savior (common to many Christian interpretations of the passage) but an evil antichrist-like king, the "little horn" of ch. 8 (a ruler from the kingdom of Greece). The installation of the desolating abomination is mentioned in 1 Maccabees 1:54:
"On the fifteenth day of Chislev in the year on hundred and forty-five [i.e. December 8, 167 BC], the king erected the desolating abomination above the altar; and altars were built in the surrounding towns of Judah".
This event is also described in 2 Maccabees 6:2 which states that Antiochus "profaned the Temple in Jerusalem by dedicating it to Olympian Zeus", and "the altar of sacrifice was loaded with victims proscribed by the laws as unclean" (v. 5). From this time forward: "The king sent instructions ... banning holocausts, sacrifices and libations from the sanctuary, profaning sabbaths and feasts, defiling the sanctuary and the sacred ministers" (1 Maccabees 1:44-46). Then, three years later and 3 1/2 years after the mysarch devastated the city and Temple, the Maccabeans rededicated the Temple and purified it (i.e. anointing it anew):
"They had overthrown the abomination he had erected over the altar in Jerusalem, and had encircled the sanctuary with high walls ... [Judas] selected priests who were blameless in observance of the law to purify the sanctuary and remove the stones of the abomination to an unclean place. They discussed what should be done about the altar of holocausts which had been profaned, and very properly decided to pull it down that it might never become a reproach to them, from its defilement by the pagans ... and built a new altar on the lines of the old one. They restored the Holy Place and the interior of the house, and purified the courts. They made new sacred vessels, and brought the lampstand, the altar of incense, and the table into the Temple. They burned incense on the altar and lit the lamps on the lampstand, and these shone inside the Temple. They set out the loaves on the table and hung the curtains and completed all the tasks they had undertaken. On the twenty-fifth of the ninth month, Chislev, in the year one hundred and forty-eight [i.e. December 164 BC], they rose at dawn and offered a lawful sacrifice on the new altar of holocausts which they had made" (1 Maccabees 4:42-53, 6:7).
Hence the festival of Dedication (= Hannukah) that Jesus observed in Jerusalem, as related in the gospel of John. This is the expected "restoration of the rights of the sanctuary" mentioned in Daniel 8:14 and the "anointing of the Holy of Holies" mentioned in 9:24, which occurs at the completion of the "seventy weeks". And indeed, this event occurred 7 years after 171 BC, the year when the last legitimate high priest Onias III was "cut off". The "stop to sacrifice and oblation" mentioned in 9:27 is not for all time (as the messianic Christian interpretation often construes it) but only for the "half week" at the end of the seventy weeks. Then the restoration of the Temple prophesied by Jeremiah would be complete. This event was also regarded by Josephus as fulfillment of Daniel, as restoring the sacrifice that the "little horn" had abolished in ch. 8:
"Daniel wrote that he saw these visions in the plain of Susa, and he informs us that God interpreted the appearance of this vision after the following manner: He said that the ram signified the kingdom of the Medes and Persians, and the horns were those kings that were to reign in them ... that the he-goat signified that one should come and reign from the Greeks ... and that from among them there should arise a certain king that should overcome our nation and their laws, and should take away our political government, and should spoil the Temple, and forbid the sacrifices to be offered for three years. And indeed it so came to pass, that our nation suffered these things under Antiochus Epiphanes, according to Daniel's vision" (Josephus, Antiquities of the Jews 10.11.7).
The concept of a sin-atoning Messiah is particularly alien to the context. The author makes direct reference to the curse in the "Law of Moses" (Daniel 9:11), and this curse states that "they must atone for their sin, for they have spurned my customs and abhorred my laws" (Leviticus 26:43). Not "A Messiah must atone for their sin", but THEY must atone for their sin. Leviticus has no concept of a Messiah, just as Daniel has no concept of a sin-atoning Messiah. In atoning for their sin, the Israelites were to "confess their sins and the sins of their fathers, sins by which they betrayed me" (Leviticus 26:40), and this is exactly what Daniel does, making his "confession" while fasting dressed in sackcloth and ashes (Daniel 9:3-4). The seventy years were a time for repentance (just as the expanded "seventy weeks" were a time for "putting an end to transgression and expiating crime", v. 24), and the prophet made his confession before the literal 70 years were over. The atoning for Israel's sin is also mentioned in Isaiah 40:2, that at the time Cyrus allows the exiles to return to Jerusalem, their "time of service is ended, that their sin is atoned for, that they have received from the hand of Yahweh double punishment for all her crimes". The difference in Daniel is that the period for atoning for sin is expanded into seventy weeks of years (Daniel 9:24), postponing the completion of atonement for several hundred years. The people atone their sins, and God absolves their guilt along the same lines as Leviticus.