Yeah, that's the thing, there's likely to be lots of different alien species, so it is indeed a numbers game. I wouldn't want to try giving the odds of each alien species discovering Go, but so long as those odds are non-zero, which seems quite likely, the total number of Go inventions across the universe is likely to be quite large.

This naturally introduces the idea of a "universality constant" for any given game, i.e. what percentage of species will have invented that exact game. For obvious reasons this figure is likely to be much higher for, say, Go, Connect-N, or Hex, than for something like Chess.