Dexter Green starts "Winter Dreams" at age fourteen and ends it at thirty-two, so he clearly comes of age over the course of the story. But Dexter's coming-of-age is not a positive triumph over his obstacles. He has to face the bitterness of losing his ideals and compromising his dreams.
The story's interest in Dexter's psychology (rather than in some exciting plot line with lots of twists and turns) indicates that "Winter Dreams" is an example of literary fiction. Fitzgerald's careful style and melancholy tone are formal storytelling elements that belong to literary fiction rather than to, say, the superhero story or the detective novel. (Dex would probably make a really lousy superhero anyway.)