The intention of the GP was - given that Go was not invented again on Earth, there's no real indication that it would be invented again at all. That doesn't imply that it cannot be invented again because it is too complex.
Also, it's kind of silly to count something not have being reinvented against it, because things almost by definition cannot be reinvented. Look at how popular board games are right now; if Go hadn't yet been invented, it's quite possible that it would be invented now. But instead it has already been invented, so people already know about it, and any would-be inventors end up not being inventors; they either already know about it or are told that what they've come up with already exists.
Well, they can, but the opportunities are limited to cultures where the game has not been introduced yet.
I would also point out that we don't know that Go was never invented independently on earth, just that it was never invented and popularized in a manner that left a cultural or historic record of which we are aware. If Go were played by a small clan of prehistoric people using different color berries and a grid scratched out in the dirt, what evidence would be left?
So that REALLY limits the opportunities to cultures that left a significant historic record but had no cultural exchange with china.
Not quite. It's making a must out of an is. The relevant distinction is "true by necessity" vs "true by coincidence", not "factually correct" vs "morally correct".
I don't want to get into arguing Drake's equation here, but if you accept that aliens exist, then you're granting that there's a lot of them; it makes no sense why we would be, e.g., one of only two intelligent species in the entire universe.
It may be wrong, but "aliens" is not a response to it.