In normal usage if someone says they're 'writing a story' that means either a traditional piece of fiction (of any length - I never said that short stories were not referred to as 'stories') or a news article. If someone's writing a play, poem or technical work, they would usually be specific about the form rather than saying 'I'm writing a story'. (I can imagine situations in which 'story' would be used for a play, film script, or narrative nonfiction piece of some kind but in general those are things that have stories rather than things that are simply referred to as being stories.) [ETA: just occurred to me that at the place I work, the articles we write are never referred to as 'stories', even when they are news pieces.]

I think there's a pretty clear slant here toward the stereotypical novel writer - many of whom do exist, but they're not the only writers who write. If you disagree, that's cool.