IMO this is clearly implicit in the "you are a grandmaster chess player" prompt. As that should make generating best possible move tokens more likely.
Is it? What if the AI is better than a grandmaster chess player and is generating the most likely next move that a grandmaster chess player might make and not the most likely move to win, which may be different?
Depends on the training data I think. If the data divides in games by top chess engines - and human players, then yes, it might make a difference to tell it, to play like a grandmaster of chess vs. to play like the top chess engine.
Grandmasters usually play grandmasters of similar ELO, so it might think it doesn't always win. Even if it should recognize the player isn't a grandmaster, it still may be better to include that, though who knows without testing.