I consider the triangular aspects A.[prisoner/captive/confined] in a B.[specific space/structure/building] and the verb C.[to escape/reach freedom/free prisoners, release from dictatorship] the main pillars of this group.
The distinction I consider fundamental is that the player even if frees prisoners or something hijacked, he was also a prisoner in the first place. He does not enter in a space with the mission to free hostages or similar, he is already inside that space being captive too.
Into the Eagle's Nest would be an example of a game which didn't belong to that group although has similar characteristics.