I'm sure people who think a lot more about roleplaying game design have spend millions of bytes on defining what a "storytelling game" is and concluded it's like pornography, you can't define it to everyone's satisfaction, but you know it when you see it. But I'm sure one thing that comes up a lot in these discussions is "narrative control."
In conventional roleplaying games there is a very clear divide between players and GM. Players control only their characters, while GMs make all the decisions about what the world around them is, how it works, what's in it, what everyone in it is doing. Players can make suggestions about these things in many ways, but ultimately the GM decides. Even when a game allows a brief and scope-limited incursion of player into the GM's "narrative control" territory, such as with plot points, the GM has veto rights over it.
Storytelling games require the players to step outside that limitation and the mindset that goes along with it, and start thinking of the world around their characters as part of their area of influence. They can decide, usually by consensus with other players, what's going on in the world around them. They can posit NPCs, frame scenes, describe the results of actions (both theirs and others), and offer ideas about what they find around them. Sometimes this is also something their characters can do (as in the case of Solipsist) but even when it's not it's something the players do. In many cases there is no GM, and everyone at the table is both player and GM.
I played a lot of these, back to back, at Carnage this year, and without any interruptions by the more conventional player-GM divide. The only thing I did that wasn't like this was Pandemic, which fails to contradict it, since it's still a group deciding things by consensus. And it seems the shift in the way of thinking wormed its way into my brain.
Monday morning the day after Carnage, on the way to work, I saw a mailbox with the name Gingras on it in those stick-on letters, and for a split second I wondered if that was the name "Gingras", or the name "Gingra" in plural (the way you see "Smiths" on the mailbox of the Smith family). All this is perfectly normal. Then for a moment I thought, "It'd be more interesting if it's the plural of Gingra, so let's say it is" and then found myself wondering why I was thinking of it as if it were up to me. As if reality itself were negotiable. And I flashed back to the games I'd been playing intensively for the previous three days, where it was, where thinking "no, this would be cooler, let's have it be that" is part of the process.
I wonder if someone who played a week straight of storytelling games might have a small dissociative break. Maybe after two weeks, you'd start getting frustrated that the world refused to become the cooler things it could be if only your ideas were able to shape it. Maybe after a month, you'd find yourself actually able to retune reality. And after two months, you'd probably end up creating a storytelling game about that.