Story writing is both linear and non-linear in nature.
The basic nature of a scenario is to relate things as they happen: A man steps on the twig. A dog barks. The man stops mid-stride.
How the story is laid out, however, need not be linear. Often it’s artfully not. My favorite example of this technique is Pulp Fiction. Early in the script we see Vincent Vega (played by John Travolta) as an accomodating fellow who has a romantic scene with Mia Wallace (Uma Therman), his boss’ girl. Later in the story we discover in a flashback that Vega is also a churlish and cold blooded killer. Had we known that in the beginning, the scene between him and Mia would have seemed creepy instead of romantic.
The nature of literary composition itself can be very completely non-linear. For, though the concept of a story may burst almost fully formed, the details will likely emerge in fits and starts triggered by events in the writers life seemingly disconnected from his/her work on the page.