When you use TimePlayed, you have to provide a game ID either when
creating the object or when calling GetTimePlayed on it. If you don't
provide a game ID when creating the object, function calls that don't
take a game ID will silently fail, except for Reload. This isn't very
obvious, and there's no strong benefit to storing the game ID inside
TimePlayed anyway (it just lets TimePlayed skip calling EscapeFileName),
so this commit removes the TimePlayed constructor that takes a game ID
and instead makes the functions that need game IDs always take a game ID
argument.