Statement

In Chess, either White can force a win, or Black can force a win, or both sides can force a draw.

Other variations

Mas Colell et al. (1995, p.272): “Every finite game of perfect information ΓE has a pure strategy Nash equilibrium that can be derived by backward induction. Moreover, if no player has the same payoffs at any two terminal nodes, then there is a unique Nash equilibrium that can be derived in this manner.”

Theorem 1 - In chess either White has a winning strategy, or Black has a winning strategy, or both have strategies guaranteeing at least a draw. The main result of this paper is as follows.
Theorem 2 - In any finite-stage two-player game with alternating moves, either
(i) player 1 has a winning strategy, or
(ii) player 2 has a winning strategy, or
(iii) both have unbeatable strategies

In all combinatorial games, at exactly one player has a winning strategy or both players have a draw strategy.
..
either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win.

Many authors claim that Zermelo’s method of proof was by Backward Induction

In his paper, Zermelo concentrates on the analysis of two person games without chance moves where the players have strictly opposing interests. He also assumes that in the game only finitely many positions are possible. However, he allows infinite sequences of moves since he does not consider stopping rules. Thus, he allows for the possibility of infinite games.