I am proposing the following language for a third win condition (changes in bold):
Elimination (The Quick and the Dead)
Elimination is the shortest format, although the high stakes elimination can discourage aggressive play.
In an elimination game, players are knocked out if they would lose by the usual metric (that is, if a player has more total control points than you have total influence at sundown, you are eliminated).
When only player remains, they win!
Apply the red rules text for Elimination games.
Victory Point (One-Eyed Jacks)
Victory Point is a medium-length format, a compromise between Elimination and Total Control.
In a Victory Point game, a player wins by earning a number of "victory points" equal to their number of opponents (ex. 2 victory points for a 3-player game). Earning a victory point is accomplished in the same manner as eliminating an opponent (using the Elimination rules), but instead of their opponent being eliminated, the player gains a permanent victory point instead. Victory points roll-over and accumulate as the game progresses. If two or more players meet this win condition at Sundown, before resolving tie-breakers normally, the player who has accumulated the most victory points wins.
Apply the [color] text for Victory Point games.
Total Control (Deadwood)
While Total Control is the longest format, everybody will be in the game until the end.
In a total control game, a player wins by beating all other players by the usual metric (that is, if a player has more total control points than each other individual player has total influence at sundown, they win).
Apply the blue rules text for Total Control games.