Previously we were requiring each player to do a separate join_game
(even after they were already part of the game). Notably, if the user
ever reloaded their browser, they had to click "Join game" yet again.
Instead, in this commit we add a game.started state. And we only need
one player to start the game, triggering the send of the started game
state to all players.
Now, if a player reloads their browser, they will just see the game
state, and not a "join game" button.