Very nice look and feel. Can I make some suggestions?
There is no real AI player is there, it’s just random placement, not even weighted. You might want to look at tic-tac-toe AI algorithms.
I don’t understand the ‘back’ of the board when you win or lose, it looks the same.
Here’s an idea to make the whole thing more engaging (since a dumb AI will always lose and it will quickly become boring to play a friend online) - make the best of being in 3D space, and make it a concurrent 6-way match, with one board on each side of the cube, and you have to play all sides at the same time (either against other players, a single other player, or an AI, or a mix).
The idea comes from watching The Queen’s Gambit last night, when she plays concurrently against the entire chess club