You could add a "back to main menu" button in game. And a singleplayer mode would also be good.
It looks clean and nice for such a simple game, and it works. The bug I found is that you're still able to make moves in between when the game is won and a new game is loaded. So it will say "Player 1 wins!" and then you make another move that wins for player 2 and it will change to "Player 2 wins!" before loading the new game.