[simorley]

> In chess, it's possible to end the game in a draw, so Zermelo's theorem does not apply to it and OPs claim is wrong about chess.

Isn't it even assumed that a perfect game of chess is a draw. Once chess is solved, it'll be all draws.

[Kranar]

Yes it's an open question. The prevailing opinion is that a perfect game ends in a draw as you said, with a minority opinion that white can force a win. I am not aware of any credible opinion that black can force a win.