I would suggest that two-person games may be on-topic if, in any situation mentioned by the puzzle, there will be some procedure by which moves can be unambiguously categorized as either "best" or "inferior"; there may be multiple equally-good "best" moves, and there might be many categories of "inferior" moves, but it must be possible to prove that a particular move is "best" [other moves may be just as good, but none qualitatively better].
I think the biggest difficulty with two-person games is that some question/answer pairs will be like
- Q: Is there a known winning strategy for game X?
- A: Sure. If a player opens with Q, then on each turn thereafter does R, victory is guaranteed.
which would be an informative Q/A pair and which--if the strategy was not obvious until demonstrated, but would be clear and understandable once it was explained--could be a good fit for a puzzle site, but others would be more like:
- Q: Is there a winning strategy for game X?
- A: As yet there is not. The second player cannot have an advantage, and no human or computer has ever beaten program Y, even when it plays second (it always manages at least a draw), but it has not yet been proven that no winning strategy exists for the first player.
or
- Q: Is there a winning strategy for game X?
- A: Computer searching has shown that the first player can always win with perfect play, but there are many situations where the proper move is far from clear. It does not appear likely that there is any simple "human-understandable" perfect strategy for the game.
While the first answer would be a good fit for the site (finding the strategy could be a good puzzle in and of itself), the latter two would suggest that the search for a perfect strategy would be more of a research project than a "puzzle". Unfortunately, I don't know any means by which someone could judge whether the answer would be a good fit for the site without knowing what the answer was; if the answer can't readily be found elsewhere, that would mean that one couldn't know whether the question would be a good fit before asking it.