OPs claim is poorly stated. He's referring to Zermelo's theorem which states that a finite game with two players that's deterministic and zero sum with perfect information and no possibility of a draw must have a winning strategy. It's not difficult to prove that this must be true and you likely can intuit why it's true (imagine building a decision tree for such a game).

But all of those qualifiers I mentioned are needed, and that's a lot of qualifiers. If any of them are no longer true then there is not guaranteed to be a winning strategy.

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.

I'm fairly certain one can trivially disqualify one of those criteria when it comes to financial markets as well.