Chess belongs to a class of games that are particularly interesting to study: it is a finite extensive form game which basically means the game can be modeled as a tree and requires only shared knowledge among participants, all the participants have complete shared knowledge, it’s sequential, has perfect recall (nothing prevents looking backwards at the game state), and a simple payoff function (you win if you checkmate the opponent, in which case the opponent also loses) that is zero-sum.

This makes it so chess has a one-shot sub game perfect equilibrium: https://en.m.wikipedia.org/wiki/Subgame_perfect_equilibrium. But, the dimensionality of the possible end states is very high, because there are many different configurations leading to a checkmate, so you can’t easily perform backward induction. But you can perform minimax (which is how Stockfish works): https://en.m.wikipedia.org/wiki/Minimax

From a game theory perspective chess is really not at all like an actual war, because the properties of the game are different in almost every conceivable way - not just because of perfect information. But, you can model more complex “games” like war in a way that makes them more similar to chess if you wish. Just be careful because ignoring very fundamental differences like the payoff model could greatly affect decision making - for war, you’d probably rather surrender or make minor concessions in most cases than win at the cost of 99% of your people and infrastructure getting destroyed.