I think that a successful short story should quickly get your attention and draw you into the story without providing too much background on the characters or the situation. A short story should be like a satisfying light snack, rather than a 6 course meal.
Most of these stories establish themselves early and give you a reason to continue. Some of them seem to be intentionally vague, allowing the reader to fill in the details on their own. Overall, I think they work very well if you've got a few minutes and want a tasty, quick snack.