Not that anyone cares or should, but I doubt that Johannine "panchristology" ("Jesus is the gate" as he is the way, the shepherd, the vine, and so on) really works in the context of Matthew. Should Jesus be thought of as the gate there he would only be so as the teacher who points to the right things to do for perfect fulfillment of the Torah (5:17ff; 7:21ff).
The teaching of the "two ways" is a most widespread topos in Judaism, which can be traced back to Deuteronomy 30:15ff and thrives in the 1st century AD (cf. 4 Esdras and its similar emphasis on the right way as narrow -- exactly one foot wide, 7:6ff, 47; cf. 8:1ff, few are to be saved). The Didachè, which offers the closest parallels to the Gospel of Matthew on many subjects (fasting, the Lord's Prayer, "trinitarian" baptism formula etc.), starts with a similar teaching (I highlight the most obvious Matthean parallels, but there would be further parallels to the epistle of James for instance):
There are two ways, one of life and one of death, but a great difference between the two ways. The way of life, then, is this: First, you shall love God who made you; second, love your neighbor as yourself, and do not do to another what you would not want done to you. And of these sayings the teaching is this: Bless those who curse you, and pray for your enemies, and fast for those who persecute you. For what reward is there for loving those who love you? Do not the Gentiles do the same? But love those who hate you, and you shall not have an enemy. Abstain from fleshly and worldly lusts. If someone strikes your right cheek, turn to him the other also, and you shall be perfect. If someone impresses you for one mile, go with him two. If someone takes your cloak, give him also your coat. If someone takes from you what is yours, ask it not back, for indeed you are not able. Give to every one who asks you, and ask it not back; for the Father wills that to all should be given of our own blessings (free gifts). Happy is he who gives according to the commandment, for he is guiltless. Woe to him who receives; for if one receives who has need, he is guiltless; but he who receives not having need shall pay the penalty, why he received and for what. And coming into confinement, he shall be examined concerning the things which he has done, and he shall not escape from there until he pays back the last penny. And also concerning this, it has been said, Let your alms sweat in your hands, until you know to whom you should give.
And the second commandment of the Teaching; You shall not commit murder, you shall not commit adultery, you shall not commit pederasty, you shall not commit fornication, you shall not steal, you shall not practice magic, you shall not practice witchcraft, you shall not murder a child by abortion nor kill that which is born. You shall not covet the things of your neighbor, you shall not swear, you shall not bear false witness, you shall not speak evil, you shall bear no grudge. You shall not be double-minded nor double-tongued, for to be double-tongued is a snare of death. Your speech shall not be false, nor empty, but fulfilled by deed. You shall not be covetous, nor rapacious, nor a hypocrite, nor evil disposed, nor haughty. You shall not take evil counsel against your neighbor. You shall not hate any man; but some you shall reprove, and concerning some you shall pray, and some you shall love more than your own life.
My child, flee from every evil thing, and from every likeness of it. Be not prone to anger, for anger leads to murder. Be neither jealous, nor quarrelsome, nor of hot temper, for out of all these murders are engendered. My child, be not a lustful one. for lust leads to fornication. Be neither a filthy talker, nor of lofty eye, for out of all these adulteries are engendered. My child, be not an observer of omens, since it leads to idolatry. Be neither an enchanter, nor an astrologer, nor a purifier, nor be willing to took at these things, for out of all these idolatry is engendered. My child, be not a liar, since a lie leads to theft. Be neither money-loving, nor vainglorious, for out of all these thefts are engendered. My child, be not a murmurer, since it leads the way to blasphemy. Be neither self-willed nor evil-minded, for out of all these blasphemies are engendered.
Rather, be meek, since the meek shall inherit the earth. Be long-suffering and pitiful and guileless and gentle and good and always trembling at the words which you have heard. You shall not exalt yourself, nor give over-confidence to your soul. Your soul shall not be joined with lofty ones, but with just and lowly ones shall it have its intercourse. Accept whatever happens to you as good, knowing that apart from God nothing comes to pass.
My child, remember night and day him who speaks the word of God to you, and honor him as you do the Lord. For wherever the lordly rule is uttered, there is the Lord. And seek out day by day the faces of the saints, in order that you may rest upon their words. Do not long for division, but rather bring those who contend to peace. Judge righteously, and do not respect persons in reproving for transgressions. You shall not be undecided whether or not it shall be. Be not a stretcher forth of the hands to receive and a drawer of them back to give. If you have anything, through your hands you shall give ransom for your sins. Do not hesitate to give, nor complain when you give; for you shall know who is the good repayer of the hire. Do not turn away from him who is in want; rather, share all things with your brother, and do not say that they are your own. For if you are partakers in that which is immortal, how much more in things which are mortal? Do not remove your hand from your son or daughter; rather, teach them the fear of God from their youth. Do not enjoin anything in your bitterness upon your bondman or maidservant, who hope in the same God, lest ever they shall fear not God who is over both; for he comes not to call according to the outward appearance, but to them whom the Spirit has prepared. And you bondmen shall be subject to your masters as to a type of God, in modesty and fear. You shall hate all hypocrisy and everything which is not pleasing to the Lord. Do not in any way forsake the commandments of the Lord; but keep what you have received, neither adding thereto nor taking away therefrom. In the church you shall acknowledge your transgressions, and you shall not come near for your prayer with an evil conscience. This is the way of life.
And the way of death is this: First of all it is evil and accursed: murders, adultery, lust, fornication, thefts, idolatries, magic arts, witchcrafts, rape, false witness, hypocrisy, double-heartedness, deceit, haughtiness, depravity, self-will, greediness, filthy talking, jealousy, over-confidence, loftiness, boastfulness; persecutors of the good, hating truth, loving a lie, not knowing a reward for righteousness, not cleaving to good nor to righteous judgment, watching not for that which is good, but for that which is evil; from whom meekness and endurance are far, loving vanities, pursuing revenge, not pitying a poor man, not laboring for the afflicted, not knowing Him Who made them, murderers of children, destroyers of the handiwork of God, turning away from him who is in want, afflicting him who is distressed, advocates of the rich, lawless judges of the poor, utter sinners. Be delivered, children, from all these.
Note both ways are described as a matter of doing, without the least reference to faith in Jesus or lack thereof.
