tictactoe: Actually toggle between X and O as the current player

It is kind of hilarious that I hadn't even noticed that up to now
every move committed to the board was an "X". I hadn't noticed this
because the server state is currently only used to determine if a new
move is legal, (in that the board is unoccupied). The code currently
doesn't test for a win, for example.

And meanwhile, the client has been tracking toggling X and O on its
own just fine.

But this will certainly be cleaner going forward, and is strictly
necessary before we serve an event that exposes the entire board
state.