Joseph: I think the reason why as you say "so many people think that our Lord will come down to rule with non-human beings" is scriptures like the ones below which seem to suggest a change from a physical (natural) body to a spiritual one:
1Cor 15:
42So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; 43it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; 44it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body. 45So it is written: "The first man Adam became a living being"[5] ; the last Adam, a lifegiving spirit. 46The spiritual did not come first, but the natural, and after that the spiritual. 47The first man was of the dust of the earth, the second man from heaven. 48As was the earthly man, so are those who are of the earth; and as is the man from heaven, so also are those who are of heaven. 49And just as we have borne the likeness of the earthly man, so shall we bear the likeness of the man from heaven.
1 Pet 3:18 For Christ also died for sins once for all, the just for the unjust, in order that He might bring us to God, having been put to death in the flesh, but made alive in the spirit
Artful