Alright, this has been percolating for a bit. I think I would go with:
Scenario Games.
Think of it as an Adventure+System. They are written to facilitate a relatively narrow story -- much like a scenario or adventure for a larger system -- but include
all the necessary mechanics and context to facilitate the game, a custom system.
Often they are structured so one person just needs to browse the book beforehand and serve as a continual in game reference much like an adventure module might. They might have a lighter GM role or be GMless.
Of some games that I think may fit this category that we carry:
Big Dog, Big Volcano -- a one-shot GMless game. One player is an oblivious hiker, one is a volcano and one is a good dog. Each player has a play sheet with slowly escalating stakes/questions/situations that they ask each other. (You just roll a die that accumulates each round, the higher your overall total, the more serious things get.)
Palanquin -- one-shot, facilitated by the player who plays the princess (closest role to GM). Story of how you saved the princess from a palace coup and whether she trusts you at the end. The other players grab up to 5 of the 6 other character archetypes and introduced threats on the journey largely based on their archetypes. The scenario part comes in with the 6 locations+themes you journey through.
Once More Into the Void -- one-shot to 6 shot. Facilitated by the captain character. A few default scenes-- character recruitment and final confrontation -- and a series of optional mini-game scenes that the players get to select. You are the crew of a starship who have saved the galaxy once before and a new threat to the galaxy has emerged. Can you put your differences aside and work together once more?
One-shot GMless games like
The Quiet Year and my own
God-Killer Prophecy almost fit here, but I think the difference is mostly in how narrow a story/scenario the mechanics can support.
@Faolyn do you think this fits some of what you are looking for?