The enotes reference section says this about the short story:

A short story is a work of fiction that is usually written in prose, often in narrative format. This format tends to be more pointed than longer works of fiction, such as novellas (in the 20th and 21st century sense) and novels or books. Short story definitions based upon length differ somewhat even among professional writers, due somewhat in part to the fragmentation of the medium into genres. Since the short story format includes a wide range of genres and styles, the actual length is mitigated somewhere between the individual author's preference (or the story's actual needs in terms of creative trajectory or story arc) and the submission guidelines relevant to the story's actual market. Guidelines vary greatly among publishers.

In other words, a short story is a work of fiction usually written in prose, without an established length.  In other words, no set length is mandatory for a story to be labeled a "short" story. 

The length depends on a writer's whims, the subject's needs, and what publishers will accept.