My God doesn't play either. I know He "causes all things to work together for good to those who" love Him and "are called according to His purpose." (Romans 8:28)
Chess has a limited number of pieces and a limited number of moves. God's plan, God's balance of the universe, God's love -- all are infinite in nature.
You are confusing a great game with God's plan for the universe. Not the same thing at all.
God would play within the rules. He would be a most awesome player. I wonder if God's first move, with white, would be P-K4 or some other opening.
Also, it has been said that there are so many possible moves in a chess game that all the moves have not been made yet.