Reign? Or Reign as Kings?
The Greek word here literally just means to ‘reign’, or rule as a king.
While those words do usually mean the reign of a king, there is some discussion over the fact that in Revelation, it sometimes describes people who are elsewhere described as princes, not kings.
Therefore, in Revelation 5:10, 20:4, 20:6, and 22:5, we just use the word ‘reign’ or ‘reigned’ without embellishing it, and leave the rest to you.
Interestingly, the word used in the Aramaic translation of Revelation can likewise meant to ‘reign’ or to ‘reign as king’, but can also mean to advise or to give counsel.