WMG: Temple Run

The explorer is already cursed to death
It happened when he/she picked up the idol. I know it's kind of obvious, but it's not outright stated in game either.

The explorer is already dead
He/She is in hell, and is cursed to eternally run an endless path in a non-Euclidean environment with no exit.

The game takes place in the Skullmonkeys universe
As you're chased by Skullmonkeys