I’ve asked this elsewhere, so apologies if you’re seeing this again!
I’m looking for storytelling games which can be enjoyed by people who have never played such games, and which aren’t technically difficult - I’m thinking of something which can serve as a stimulus for different people in a group to tell their own stories, and maybe have something (physical and/or which can be displayed) that can come out of it at the end? Can you think of any?
Assuming you’re not looking for something digital, I suggest The Quiet Year. It’s a paper-and-pencil game where you sit down and talk through the experiences of a community over the course of a year, and when you’re done, you have a map of the world you built.
I haven’t played the others, but I don’t think I’d call Betrayal at the House on the Hill a storytelling game. Any sense of story it creates is purely a matter of mechanics; players don’t actually contribute to the story themselves any more than they do in a game like Arkham Horror or Shadows Over Camelot.
As for suggestions, there’s a local designer here who focuses on this kind of thing. His latest is called Faith, and I haven’t played it but it sounds like exactly what you’re looking for (if you like the gangster movie theme, anyway).
It might be a matter of the Tabletop players hamming it up…such as Felicia Day in Last Night on Earth coming up with motivations for her Dr Zombie rolls. Lots of tabletop games lend themselves to improv story play. Even my group with Love Letters came up with some hysterical dialogues regarding who they were consorting with at any given time.
Microscope probably requires at least one player to take the time in advance to get a grasp on the rules, but I can attest that I was able to enjoy it as a player with fairly little introduction.
Re: Betrayal and Arkham Horror: I love both of these games (for example, my Arkham Horror group is a force to be reckoned with) but they aren’t innately storytelling devices. It’s awesome when they are, but it isn’t automatic (for example, my Arkham Horror group is a force to be reckoned with… because we do a lot of math).
Have you tried Fiasco? You roll some dice to get a character, and then roll for some different scenarios, and tell a story together. The mechanics really lend themselves to conflicting motives and grandiose plans and funny stories.