Easy. Any biometric sensor. Fingerprints for instance. If the machine detects the same person trying to play again, it just refuses to run. Or... (if I was designing this) kills them where they sit. Next person that reaches the game's remote location gets to remove the skeleton from the chair. Good incentive to not cheat.
(I'm assuming some kind of real-world post-apocalyptic scenario, in which 'legal ramifications' don't exist.)
Actually, if there was some decently functional strong AI in the game, this could get very mythological. Quest to visit the Oracle - you have to get to the site then play the game in order to reach the Oracle in the gameworld. If you die in-game before then - well tough.
Sadly, I don't see how you could hope to enforce this constraint... The idea of a game seat is nice, though -- a collaborative time capsule of sorts.