Does it? A lot of concepts in board games are pretty natural results of universal mathematics. There's only three regular polygons that will tesselate a board (we have plenty of board games that use all three of them), and there's only three dimensions that games can work in (and we have plenty of games of all three types; Candyland, for instance, is played along a 1D path, and the first player to reach the end wins).
Even if some aliens think so differently from us that the concept of a square is unknown to them, surely there are plenty of aliens that would think similarly enough?
You're assuming a lot about what it means to be an intelligence. It's not the concept of a square that will potentially be missing from an alien lifeform. It's the complex circuitry involved in enjoying board games in the first place. One can imagine an intelligent lifeform evolving differently than us in such a way where the adaptation that makes games fun wasn't required.
If they have a civilization, they probably are social creatures, and thus probably enjoy playing. Most social creatures on Earth engage in play when they are young. Also, for many animals, playing helps them learn how to hunt.
Of course not all of them, we enjoy games, and we're the only actual data point we have. But since we're just one data point, we really don't know anything about the probability of different subsystems of the mind evolving. I certainly hope we encounter sentient empathetic aliens that enjoy games as much as we do!
Well for Go to not exist anywhere in the universe there'd either have to be no aliens, or no aliens that enjoy games, or something along those lines. So long as there are some aliens and some aliens that enjoy games, Go and other relatively simple abstract board games do seem like they should inevitably be reinvented many times over across the universe.
Hell, maybe there's aliens that don't enjoy games per se but that use them for other purposes, like deciding legal guilt or who gets to rule.
Even if some aliens think so differently from us that the concept of a square is unknown to them, surely there are plenty of aliens that would think similarly enough?