Why are people so quick to assume that every single other alien species would be completely unfathomable to us? We all share the same physics, chemistry, and mathematics of our common universe. For example, there's only three dimensions, and there's only three regular polygons that can tessellate a grid. Unless you're going to posit that there's no alien species whatsoever that will even come up with the concept of a game (which I find highly doubtful), they're going to be using the same abstract mathematical concepts as we are in building said games, because only so many abstract mathematical concepts even exist.
Our simplest board games aren't that far removed from the realm of the purely mathematical. And yet aliens won't all have their own completely different mathematical systems; such a thing isn't possible.
Our simplest board games aren't that far removed from the realm of the purely mathematical. And yet aliens won't all have their own completely different mathematical systems; such a thing isn't possible.