Edgar Allan Poe has been called the father of the modern short story. He defined the short story in a famous review of Nathaniel Hawthorne's Twice Told Tales. Part of his definition is as follows:
A skilful literary artist has constructed a tale. If wise, he had not fashioned his thoughts to accommodate his incidents; but having conceived, with deliberate care, a certain unique or single effect to be wrought out, he then invents such incidents, he then combines such events as may best aid him in establishing this preconceived effect. If his very initial sentence tend not to the outbringing of this effect, then he has failed in his first step. In the whole composition there should be no word written, of which the tendency, direct or indirect, is not to the one pre-established design.
A perfect short story would create a single effect, and there should not be a single word in the whole composition which did not tend to that one pre-established effect. The "effect" is the feeling the reader is left with upon finishing the story.
The chilling effect in "The Cask of Amontillado" is strong and unmistakable. The story is quite short and arguably does not contain a single unnecessary word or leave out a single necessary detail. It serves as Poe's best example of his own definition of the modern short story. A reader can test the story by picking out any detail and asking whether it is essential and why. Many readers have asked why Poe didn't offer at least a few examples of the "thousand injuries of Fortunato" that led Montresor to plot revenge. Poe evidently left them out because he did not feel they were essential to creating his single pre-established effect.
Edgar Allen Poe is the father of short story, and "The Cask of Amontillado" is considered as one because it has unity of effect and it moves you from 2 contradictory settings without having gaps. That is one ;)