You could implement player-submitted AI as a web API - so they would write something in whatever language they choose, deploy it on Heroku, or now.sh, or stdlib or whatever, and then provide the URL.

When it's time to make a move, you just call their URL and process the response.

I don't think games involve a lot of data right? So you could probably make it stateless by transferring the whole game each time.

If you want a hand with this I could probably help! Just reply here, and I'll drop you an email.