I checked the Revelation Climax book and it doesn't draw any christological implications from the passage.
It is true that Revelation has a (subordinationist) binitarian christology that at least in its present form posits a close unity between Jesus and God: (1) the "Lord God Almighty and the Lamb" together comprise the eschatological "Temple" (21:22), (2) both the Father and the Lamb sit on the "Throne" (3:21, 7:17, 12:5, 22:3), (3) salvation belongs only to "our God who sits on the Throne and his Lamb" (7:10), (4) both the Lamb and the Lord God are called the First and the Last and the Alpha and the Omega (1:8, 17, 2:8, 21:6, 22:13; cf. Isaiah 41:4, 44:6, 48:12 in which "First and the Last" is an expression of Yahweh's uniqueness as God, which is clearly the inspiration of "Alpha and Omega"), (5) both the Lamb and the Lord God shine providing light in place of sunlight in New Jerusalem (21:23, 22:5), and so forth.
It is however somewhat unclear what is meant in 11:15-17, as there is an apparent lack of grammatical agreement in v. 15: "The kingdom of the world has become the kingdom of [our Lord and his Christ] (plural entity), and he (singular) will reign forever and ever". This phrasing is odd because if both are reigning together, the plural verb would be expected (and throughout Revelation, Jesus and God are separate entities); the third person singular future verb basileusei "he will reign" in v. 15 has as its antecedent either "Lord" or "his Christ" but not both. Thus it has been frequently suggested that "and his Christ" is a harmonizing gloss that inserts a reference to Christ in a passage that has only God in view. Indeed, there are many similar passages that are thought to be Christianizing additions, such as the tangential way the Lamb is mentioned in 15:3 ("They sang the song of Moses the servant of God and the song of the Lamb", compare the ancillary way the Lamb is mentioned in 7:9-10, 22:1, 3). And the intertextuality latent in the passage clearly suggests that kurios "Lord" is what goes with basileusei (cf. Exodus 15:18 LXX, Psalm 10:16 LXX, Psalm 146:10 LXX, Zechariah 14:9 LXX, Wisdom 3:8, etc.), indicated as well by the statement in v. 17 that "Lord God" (kurie ho theos) has "begun to reign (ebasileusas)". So I think the passage isn't necessarily christologically meaningful, if "and his Christ" is a paranthetical gloss. However it may have an OT intertext of its own, as suggested by this comparison:
Psalm 2:2 LXX: "The kings of the earth took their stand and the rulers were gathered together against the Lord and his Christ" (kata tou kuriou kai kata tou khristou autou). Psalm 10:16 LXX: "The Lord will reign forever and ever" (basileusei kurios eis ton aióna kai eis ton aióna tou aiónós).
Revelation 11:15: "The kingdom of the world has become the kingdom of our Lord and his Christ (tou kuriou kai tou khristou autou), and he will reign forever and ever (basileusei eis tous aiónas tón aiónón)".
