​SOS/Septentrion (SNES, 1993)

Good sense of vulnerability and impending doom (the ship becomes more wrecked as time passes)
Four different playable chars (they play the same but a few things make the experience different: different intro story, different start locations, somewhat different paths through the game (sometimes different methods are needed to save certain survivors) and different relatives to save))
No permanent abilities or tools gained (besides keys and maps)
Layered world (see Goonies 2)
Three different endings (better if you manage to save your char's relatives, best if you also save the other 7 survivors)
PoP-style controls but with some mid-air control
Unlimited lives but you'll lose 5 minutes (you have about an hour to escape)
Die from falling about a screen's length or more
No save feature (short game though)

Influenced by: Probably Prince of Persia

Influenced: Septentrion: Out of the Blue, possibly Disaster Report, Rain World