It would surely just be fluff in the prompt. The model's ability to generate chess sequences will be bounded by the expertise in the pool of games in the training set.

Even if the pool was poisoned by games in which some players are trying to lose (probably insignificant), no one annotates player intent in chess games, and so prompting it to win or lose doesn't let the LLM pick up on this.

You can try this by asking an LLM to play to lose. ChatGPT ime tries to set itself up for scholar's mate, but if you don't go for it, it will implicitly start playing to win (e.g. taking your unprotected pieces). If you ask it "why?", it gives you the usual bs post-hoc rationalization.