There's are a lot of posts regarding narrativist games. I browsed them and came away with the feeling that narrativist games appeared out of nowhere in the last few years and were a movement away from simulationist or 'gamer' games. I exaggerate but you get the idea. It's bullshit frankly. I am an old school gamer but let me tell you I wasn't a roleplayer until I started to spin a story.
You don't need rules or mechanics to give your game a narrativist spin. Stories grow out of the interaction of players and referee and their actions and outcomes. One of the best examples of this I ever saw was in an issue of The Dragon where the author generated a character while using results to create a compelling backstory with more hooks than Pinhead the Cenobite on a tear (The Strategy of Survival, Dragon #18).
Setting out to tell a story (whether you are the referee or a player) is a mug's game. Maybe the story you want to tell doesn't interest anyone else ('Mime is an epic tale telling how I seized the throne of the Galactic Empire!') Being as inclusive as you can helps but believe me, you always get that one player who marches to his own drum ('You'll make me a grand duke? I still don't want to help you conquer the galaxy. I want to loot it!') Stories happen naturally enough. You just need to keep an eye out for them and give them some loving and attention.
Every time a player wants to take an action and the referee says, 'Tell me how you'll do it.' the player is offered an opportunity to tell a story. Some systems like Atomic Sock Monkey's PDQ have mechanics to reward good roleplaying (or strategy or whatever you want to call it to keep the simulationists happy).
In my experience storytelling was lightning in a bottle. It arose of its own accord. It's very hard for a referee to run characters through a story because as I said their players will almost certainly have their own plans. Like it or not the players have an effect on the game world, and they should. The moment you start running a game that setting you worked on becomes a collaborative effort. IMO that's doing it right. If you are a diehard storyteller then your choice is either railroad the players into your plot or let them be spectators as the story unfolds. I had a referee take the latter approach with his Star Wars game. We weren't the heroes because we didn't have a movie about us. It wore thin after a while. I mean we had a whole fucking galaxy to romp around in. Let us free a planet or blow one up. Who said Luke or Vader ever had to deal with it? Figure about ten worlds in the SW galaxy were wiped out by novas and asteroid impacts every year alone.
Some games take the point of view that the characters are the be all and end all. Everything revolves around them and their story, assuming they found common ground ("Help me conquer the galaxy and you can loot whoever opposes me after my fleet softens them up.") I think this approach can be taken too far. Some things are always beyond your control. There are other people in the world executing their own plans. You are never the only story (the other stories are just happening offstage for the most part.)
The point I want to make is any game can tell a story. Mechanics are irrelevant to the stories being told. Having a game fall into a certain category is a convenient label that gives an idea of its primary focus. It isn't a cage.
Finally if you want to tell your own story, one that you feel strongly about; that's called writing. Try it.