Your task is to break out of a prison or similar institution. Be this the main point or not.
The first video game about Prison break was released in 1982.
For any kind of imprisonment, penitentiary for the criminally inclined or a mental ward, as long as you escape from the jailors. Simply having a prison as a level and escape being committed there is not enough, the character or characters need to have been imprisoned there as well, and not by just some natural or unnatural disaster that trapped them in there.