What do Jehovah's Witnesses say about Matthew 16:28?

Your main question (What do Jehovah's Witnesses say about Matthew 16:28?) has been answered but this has nothing to do with October 1914 when the Witnesses say Jesus began to rule, invisibly, from heaven. The disciples who were present when Jesus was transfigured were “anointed” Christians, part of the 144,000 class with a heavenly hope, those who reign with Christ Jesus from heaven. They died before the Son of Man came into his Kingdom and would have to wait till 1914 before being resurrected to heaven.

For clarification, the Witnesses believe there is only one class of “anointed” Christians, those of the 144,000 who have a heavenly hope. The other class of Christians are those who have an earthly hope, and they are not “anointed” (or born again with the Holy Spirit).

Even though there were more than two hundred thousand Christians in the first four centuries, the Witnesses believe that only a very few of them were part of the 144,000 “anointed”, heavenly class. The disciples who witnessed the transfiguration would have been part of that heavenly class. But as for the thousands of other Christians who died as a result of persecution, the Witnesses claim “The victims are identified as “professed Christians”, not Christians in fact.” Apparently, only a handful of Christians back then would have had a heavenly hope. The following quotes show the Jehovah’s Witness view:

Watchtower September 1, 1951 article ‘Hated for His Name’ page 518: “Diocletian assumed the crown A.D. 284. At first he seemed friendly to the Christians, but in the year 303 he gave in to persuasion and opened the tenth persecution, probably the most ferocious of all. Suffocation by smoke, forcible drinking of melted lead, mass drownings and burnings, breaking on the rack of men and women alike ran the empire with blood. In a single month 17,000 were slain. In the province of Egypt alone, 144,000 such professed Christians died by violence in the course of this persecution, in addition to another 700,000 who died as a result of fatigues encountered in banishment or under enforced public works.”

Watchtower January 1, 1952, page 62 - Questions From Readers: According to the article “Hated for His Name” in the September 1, 1951, Watchtower, hundreds of thousands of Christians died in the “ten persecutions” starting in Nero’s time, 144,000 dying in Egypt alone during one of the persecutions. How can this be harmonized with the Scriptural limitation of 144,000 placed on the number being in Christ’s body, and which position was the only one open to Christians during those centuries?—J.A., Dominican Republic.

Answer: “The article did not class with any finality the individuals that died during these persecutions, but spoke of the results in a general way. Note that a key qualification was made in the case referred to in the question: “In the province of Egypt alone, 144,000 such professed Christians died by violence in the course of this persecution, in addition to another 700,000 who died as a result of fatigues encountered in banishment or under enforced public works.” The victims are identified as “professed Christians”, not Christians in fact. Many of those persons might have been caught in the wave of persecution, but may never have actually preached the truth or followed in Jesus’ footsteps, being only professed Christians. They knew the world they lived in was rotten and they were listening to the message of the Christians and willing to die for it even though not in line for the high calling in Christ Jesus. Many professed Christians today might be willing to die for their faith, but still not be Jesus’ footstep followers and meeting the Scriptural requirements for such.”

Were the disciples standing there part of the first anointed class or part of the second anointed class? According to the beliefs of Jehovah’s Witnesses, the answer is neither – they were part of the ONLY anointed class, the 144,000 who have a heavenly hope. And as for Moses and Elijah, they were no part of the anointed 144,000. According to the Jehovah’s Witness teachings about the resurrection, Moses and Elijah, their appearance at the transfiguration was symbolic. They are still dead and will have to wait for a future resurrection when they will return to earth in physical bodies:

When Jesus Comes in Kingdom Glory: 9 Jesus was not alone in the transfiguration. Moses and Elijah were seen with him. (Matthew 17:2, 3) Were they literally present? No, for both men had long since died and were asleep in the dust awaiting a resurrection. (Ecclesiastes 9:5, 10; Hebrews 11:35) Will they appear with Jesus when he comes in heavenly glory? No, because Moses and Elijah lived before the heavenly hope opened up to humans. They will be part of the earthly “resurrection of . . . the righteous.” (Acts 24:15) So their appearance in the transfiguration vision is symbolic. Of what? Moses and Elijah foreshadow the anointed remnant in the time of the end. Source: https://wol.jw.org/en/wol/d/r1/lp-e/1997362

That Watchtower article helps to answer your main question, “What do Jehovah's Witnesses say about Matthew 16:28?”