Most things in games, Face Off included, happen conditionally. Do x if y happens. Or under q conditions you may do r. The Ark of the Covenant makes a declarative statement. Kick someone out of the Power Tree. Boom. Done.
True story, I once saw a Cowboy player who was dominating the HQ, use the Ark to kick Billy back into the discard pile so he could be used again in a Face Off.
Do you have to fight a bunch of snakes to get that card?