The key concept to understand the difference between RPG's fiction and written fiction is that of **authority**.

In a written story, trivially the author has authority over main characters and the environment, so she can optimize the sequence of events (the plot) to heighten the emotional impact for the reader (if she knows what she is doing).

But let's not forget that RPGs were invented to mix the experience of war games with the emotional appeal of written fiction.

In war games, the environment is fixed, and each player has authority over one and only one character (whether an army or a single person doesn't matter). To mix this with the kind of flexibility the story in a book can have, the most natural step is to simply give authority over environment to another player. 
Thus the concept of Game Master is born: it's the single person who has the responsibility of setting-up a situation, gather the reactions of other players, and let the **game mechanics** decide the result.

There is a problem though: since **dice have no sense of aesthetics**, it can often be the case that a satisfactory resolution of a conflict is spoiled because excessive bad or good luck. The Game Master is then given authority over rules, so she can bend or ignore them for the sake of the story. This is the modern understanding of the GM: the player with authority over rules and environment, with the implicit responsibility of the plot.

However, once you explicitly recognize this, you can start playing with the structure.

You can, for example, remove the authority over rules, keep the GM's authority over environment, and come up with game mechanics that automatically steers the story in an interesting and balanced direction. Games like *Dogs in the vineyard* or *Apocalypse world* retain a traditional role for the GM (minus rule-bending) while employing narrative conflict resolution (the so-called **narrative games**).

Or you can have chance-based conflict resolution but share the authority over environment and characters between active and non-active players, usually in a turn-based structure (the so-called **master-less games**). If I'm not mistaken, *Polaris*, *Shock* and *Dirty secrets* follow this structure.

Other games employ both: *Fiasco*, for example, has a turn-based shared authority with a bare-bone narrative conflict resolution; it is thus in the category of **master-less narrative games**.

All these approaches produce different kind of stories, aimed at different kind of emotional impact: written fiction is (supposedly) maximized for the passive consumer, who has no responsibility. RPGs, on the other side, optimize for immersion and responsibility, and regulate the unfolding of the plot by mechanic means, sharing authorities in different ways.