A typical approach would be to set up a contract that accepts stakes from two players per game and then let's them each make moves as they go. The contract would forward the pot to the winner.
A non-obvious but easily addressed issue is the "sore loser" problem. A player who can see he isn't going to win never takes his turn. You just make the contract declare that player forfeits the game after a little time.
A single contract could track many games in progress, with many pots. If you were really serious, you could have players upload funds once into a player account so movement of funds internally is mere accounting. Players would cash out when they don't want to play any more.
There are some jurisdictional regulatory issues outside of the purely technical issues. Caution with that.
Hope it helps.