A decent idea, save a click.

What I don't like is the algorithm which chooses what the next game is. If you have some number of games -- say 20 -- which are waiting for you to move, and some opponent who is online, moving at the same time as you, then you end up doing nothing but making moves with each other, due to the "next game" routine bringing that one (or a few) game(s) back up.

What it should do is choose the game wwaiting for your move which has been waiting the longest. That way cycling through all the games in turn, instead of fixating on one ...