This is cool, though it should be possible to create a cross-device URL for people who don't want to register. For example in chess, you'd generate two URLs, one for you and one for your opponent.
http://breakbase.com/<game_id>/<opponent_1_id>/
http://breakbase.com/<game_id>/<opponent_2_id>/
Also, are you using any pre-existing game engines, or did you write them from scratch?Would love to see diplomacy on there.