[lntue]

Your intuition is actually proved mathematically for two-player games of perfect information (even for infinite games), in which chess is included, by Wolfgang Schmidt (Theorem 7 in https://www.jstor.org/stable/1994619). Roughly speaking, if a two-player games of perfect information has a winning strategy (which might need all previous moves of a play to make decisions), then it has a positional winning strategy, which only need the current state/position to make decisions. The `only` requirement needed for that theorem is the Axiom of Choice / Well-ordering Principle.