Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Maybe we're just being thick-headed, but dissecting "A Clean, Well-Lighted Place" in terms of plot analysis just looks flat-out impossible to us. The kicker is, the story is nothing but a sequence of situations – we don't ever get any kind of action, nor do we really "learn" about the motivations of all of our characters in depth. We're not sure what they're looking for or hoping to accomplish, and the best we can do is come up with our own reasons for why they are how they are. Hemingway leaves us wondering a lot at the end of the story, but doesn't come out and resolve anything for us.