Refactor most usages of "Game" to "Room"

[AlecM33]

"Game" is no longer strictly accurate for modeling what we are doing. What we have now are "Rooms" accessed via a code, and any number of different games can be started and ended within the same room. Thus, for example, the resource should not be of the syntax /game/{access-code}, but rather /room/{access-code}. Refactor anything that doesn't align with this convention.