What does "each other player" mean on Unwinding Clock?
You untap your artifacts during player two's untap step, player three's untap step, and player four's untap step.

This isn't anything that's in the comprehensive rules or anything, it's just the meaning of the words on the card. "Each other player" could be explained as "each player who is not you" or to be really clear "every single player who is not you". None of those players is you, so you untap your artifacts during each of their untap steps.

I think you might have been wondering whether "each other" meant alternating (yes 1, no 2, yes 3, no 4...) like "every other" sometimes does. But "each other" doesn't ever mean that, so there's no ambiguity here!

You can see this demonstrated indirectly a few places in the rules, for example:


  103.4. ... First, the starting player declares whether or not he or she 
  will take a mulligan. Then each other player in turn order does the same. ...


Obviously that applies to all players, not alternating players! And of course, all the cards that say "each other player" wouldn't really make much sense if they meant alternating starting with you - in a two player game, that'd be just you.