If Ink-Eyes brings a creature back and then her owner loses in a multiplayer game, does the rezzed creature go to graveyard?
It will be exiled. The card would go back under your control if there was a temporary effect granting your opponent the control of your creature, e.g. Mind Control or Act of Treason. This is not the case, so the object under your opponent control would be exiled (since it is not the object he owns and it doesn't leave the game). The ruling in question has an example that covers it:


  800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player
  control of any objects or players end. Then, if that player controlled
  any objects on the stack not represented by cards, those objects cease
  to exist. Then, if there are any objects still controlled by that
  player, those objects are exiled. This is not a state-based action. It
  happens as soon as the player leaves the game. If the player who left
  the game had priority at the time he or she left, priority passes to
  the next player in turn order who’s still in the game.
  
  ...
  
  Example: Alex casts Bribery, which reads, “Search target opponent’s
  library for a creature card and put that card onto the battlefield
  under your control. Then that player shuffles his or her library,”
  targeting Bianca. Alex puts Serra Angel onto the battlefield from
  Bianca’s library. If Bianca leaves the game, Serra Angel also leaves
  the game. If, instead, Alex leaves the game, Serra Angel is exiled.