Are they pretty specific? It seems to me the concept is pretty general (and yes I'm familiar with the game): two players alternate placing stones on a square-tesselated board, with surrounded stones being removed from the board, and when the board is full the player with more stones wins. The no board state repetitions rules are just a natural evolution of the basic rules in order to prevent stalemates so that games actually end (and plenty of other human games have similar rules to prevent stalemates; it seems to be a generic, widely-applicable solution). Yes, there's some nuance in how scoring works (and we have multiple different scoring rules just here on Earth right now, more if you include the historical ones), and we don't actually play to the end but instead stop early once the result is clear and then calculate what the end score would've been, but those don't change the game that much and all would be considered Go.

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.