One player plays as the evil guerilla syndicate known as “The Game” or, more casually, “the overseer”. Henceforth they are not referred to as a “Player”.
It might be better to use a word that meant "players that aren't the bad guy player", such as "heroes" or "good guys", rather than use "players" to mean two different things.
Basically, to win, reach the Headquarters and defeat The Game before The Game defeats you.
This isn't true for one player.
Maybe it also should specify whether the good-guy players win or lose together, or whether there can be an individual good-guy winner.