Winning is everything -- and nothing.
Losing is nothing -- and everything.
All that matters is the game.
The Players have decided on an Endgame. Play ends only when one side has been annihilated -- even if the entire planet is destroyed in the process. They weren’t expecting the Doctor to be one of the pieces -- and neither was he. He really doesn’t want to get involved.
The Doctor doesn’t know who he is -- but he’s fast ceasing to care. Caught up in ennui, nothing seems to matter to him...