This looks very cool. I play a lot on http://iggamecenter.com, which has a zillion games, but is kinda clunky and does have the extra friction of requiring players to create an account first. What you've made is definitely better for the use-case of IMing someone a link to play.

However, if you add the ability to find other players on the site/play a random person, as has been suggested here, I think you may find that accounts being optional is a downside. Some people will make one move then leave, or just play very slowly and poorly. An account system where you can see stats on someone's past games helps avoid that un-fun situation.

The game I would most like to see you add is Hex. https://en.wikipedia.org/wiki/Hex_%28board_game%29 Maybe Dots and Boxes would be nice too as a casual game that can be played quickly, but has a bit of depth.