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I believe these passages do refer to the coming kingdom of which some of the disciples would get a preview in the transfiguration that immediately followed. But this does not negate the reality of a future millennial reign of Christ as it is clearly taught in Revelation 20. Revelation specifically speaks of a literal thousand-year reign of Christ on earth. Some, however, spiritualize this and many if not most of the books of Revelation. In other words, they take the Bible in a normal way until they come to prophecy, and then they spiritualize the prophetic passages to fit their bias.
To answer your question, I’ll just include comments from some commentaries on these verses.
16:27-28 (Mark 9:1; Luke 9:26-27). As Jesus continued to instruct His disciples, He spoke prophetically of His second coming when He, the Son of Man, would return in His Father’s glory with His angels (cf. Matt. 24:30-31; 2 Thes. 1:7). As “the Son of . . . God” (Matt. 16:16) He possesses a divine nature, and as “the Son of Man” He possesses a human nature (cf. comments on 8:20). At that time the Lord will reward His servants for their faithfulness. Speaking of His return led Him to state that some disciples standing there with Him would be permitted to view His coming kingdom before they experienced death. This statement has caused many to misunderstand the kingdom program, for they wonder how the disciples saw the Lord coming in His kingdom. The explanation is found in the following event, the transfiguration (17:1-8). [Walvoord, John F., and Zuck, Roy B., The Bible Knowledge Commentary, (Wheaton, Illinois: Scripture Press Publications, Inc.) 1983, 1985.]
28. To stress the reality of his coming and kingdom as an incentive to men to follow him, even in suffering, Christ gave the promise of verse 28. This coming of the Son of man in his kingdom is explained by some as the destruction of Jerusalem and by others as the beginning of the Church. But referring it to the Transfiguration meets the requirements of the context (all Synoptists follow this statement with the Transfiguration, Mk 9:1; Lk 9:27). Furthermore, Peter, who was one of those standing here, referred to the Transfiguration in the same words (II Pet 1:16-18). Chafer calls the Transfiguration a “preview of the coming kingdom on earth” (L. S. Chafer, Systematic Theology, V, 85).
17:1-13. The Transfiguration. At this strategic moment in the ministry of Jesus, when he had evoked from Peter the true designation of himself (16:16), and had announced his coming death and resurrection, there was granted to three disciples this most remarkable experience. [Everett F. Harrison, The Wycliffe Bible Commentary, New Testament, (Chicago: Moody Press) 1962.]