It's a common misconception that chess, GO is NP-hard. Generalized chess may be NP-hard. Chess has an 8x8 board, generalized chess has an nxn board with many pieces. The question is, given a certain position on an nxn board, will white win if both players play perfectly? There may be a "yes" answer and the certificate for NP might be a list of perfect moves for both players, but it's intractable to check if those moves by black are actually perfect. Maybe black has better moves so that white doesn't win. You can't check such a certificate in polynomial time.
Chess and Go are both EXPTIME complete. IIRC, Go has more possible moves, so I think it a higher multiple of that complexity class than chess. Wikipedia has a good article on the complexity of Go.