Just how many Elves?

This probably won't mean much if you haven't read the article, but:
Where it's telling the story of the Elves' first awakening, it says:
"In the story, Imin, Tata, and Enel wake up in that order. "
Were these the three Elven-kings that the poem describes? Because although at the time of the setting of the trilogy, the three Elven ring-bearers are Elrond, Galadriel and Gandalf, a) Gandalf's not an elf and b) Galadriel's not a King. And nor's Elrond for that matter.
So are Imin, Tata and Enel the three original elven ring-bearers?
Thanks for any replies,
Esgalfangiel