Copy several game-state members into client state

The server has been telling us (or trying to at least: see recent bug
fixes with JSON serialization of Set objects) the lists of players who
are in the process of answering or judging within the game-state
object, but the client has been ignoring this.

Without this fix, reloading of a status page could cause names to
disappear from the "still waiting" lists or the "move on" buttons.