So, strap in and let me tell you a story about storygames from an old Forge hand -- this is going to be a long post, and will differ from the people who consider all makers of storygames or their predecessors, Indie Games, swine. To start out, there were two movements, both championed by the same guy, Ron Edwards.
The first movement was that of Indie role-playing games: the idea that, rather than contributing to a larger publishing house's "supplement treadmill", someone who was interested in writing for role-playing games should write their own material and publish it themselves, maintaining control over the role-playing material that they wrote.
The second movement was a theoretical one -- the infamous GNS theory, proposed in a series of essays that started out with a deep dissatisfaction with the way the World of Darkness (1.0) promised one gaming experience in it's flavor text and delivered a completely different experience because of the mechanics. The central conceit of GNS theory was that, in order for play to be enjoyable for a play group as a whole, the play style of an rpg had to pursue one of three goals: a Gamist, win against the system, goal; a Narativist, tell a story, goal; and a Simulationist, reflect a detailed game world, goal. How much of this was supposed to reflect player preferences vs. what was rewarded by the game system vs. a weightless, spherical elephant, was left really unclear in the initial essays. Eventually GNS was morphed into what was called The Big Model, which swapped out the GNS "goals" for a "Creative Agenda" that included G, N, or S as one of its highest levels of preference (now clarified to explicitly talking about game design goals).
Of course, one of the first things that happened was the combination of Edwards' interest in the Narativist goals (and his insistence on a peculiarly rigid definition of "Story") and his promotion of independent games that he liked on his website meant that a bunch of games got labeled Narativist, and found enthusiastic support on the Forge forums. So, you had things that pushed the edges of what an rpg was combining with attempts to build a roleplaying game session that would reflect his particular definition of story: introduce characters, introduce conflict, rising action to a climax, and denoument all around a moral theme that is phrased as a question.
Other people, meanwhile, were trying to figure out what the bones of an rpg even were. Questions of who gets to say what when in a session led to what became called "The Impossible Thing [Believed] Before Breakfast" -- the conflict between the GM being in complete control of the whole game world and the Players being in complete control of their characters -- and a rejection of such techniques as railroading, the "Roads to Rome" false sandbox, and similar places where game masters use their authority to limit the players choices.
One conflict that came out of this was the people who were like, "but I like my D&D/World of Darkness/Palladium/Hero Games/etc. game, why should I care about what your theory says?" And Ron Edwards, I shit you not, says "If you play this other way, it will cause brain damage such that you won't be able to recognize an actual story when you see it. No, I won't tell you why I think this, because I get paid as a professor to explain it." Which led to a ton of hard feelings.
In another direction, Vincent Baker of Lumpley Games, particularly famous nowadays for the Powered by the Apocalypse games, started a group around the concept of storygames and the Lumpley Principle (Nothing enters the Shared Imaginary Space where a roleplaying game exists without the consent of all of the players) and used his soapbox to push the idea that traditional GM powers could -- and perhaps should -- be divided among the play group. His first rpg, kill puppies for satan put a lot of power into the hands of the players compared to D&D, and Dogs in the Vineyard and Apocalypse World continued that pattern. Other members of the Storygames coalition followed similar experimental paths that led to at least one of them claiming that they no longer considered their work a Roleplaying game, but exclusively a Story Game. Which also didn't help the traditionalist crowd, who thought they were being accused of having "badwrongfun".