The word “kingdom” properly rendered here is royal majesty. Continuing the narrative on down into the next chapter, it is stated that six days afterwards, the Lord took Peter, James and John and went apart from the rest of the disciples up into a high mountain and was there transfigured before them. His face was gloriously illuminated and became as resplendent as the sun, while his raiment was white as the light. The royal majesty of the Lord’s appearance, together with the “vision” of Moses and Elijah, and the bright cloud over-shadowing all, formed an overwhelming arrangement of light and glory. 

The Apostle Peter afterwards, in writing of this glorious scene, declared that they were eyewitnesses of the majesty (royal majesty) of the Lord Jesus, and that they also heard the voice of the Heavenly Father coming from the excellent glory (2 Peter 1:16-18). In this way, Matthew 16:28 was fulfilled.