We're talking about hypothetical alien species here. But yes, Go is a purely mathematical game. If you don't have amazing memory you can represent those bits

We're talking about hypothetical alien species here. But yes, Go is a purely mathematical game. If you don't have amazing memory you can represent those bits in a computer and it's still the same exact game. The physical board is just a physical representation of Go; it's not an actual relevant part of it (compared with, say, billiards). But yes, there are even some people that can play Go in their head. You're wrong about the amount of information though; each piece on the board has 3 potential states, not just two. Though you can chunk the board pretty effectively and it becomes more about memorizing larger patterns than the state of every single spot on the board. Plus, the board never fills up, so you only need to remember the spaces with pieces in them, not every space.