This question is asking 3 different things. The first question is whether or not you, the reader, think "A&P" is a good story. This is entirely up to individual reader opinion. Personally, I love this story. I think it's well written for a number of reasons, and I think the characters are wonderfully created. I've had colleagues who completely disagree with all of that too, so it really is up to reader opinion as to whether or not this story is "good."
Regarding whether or not it is a solid example of realistic fiction, I would have to support that argument. Realistic fiction is a somewhat wide open genre, so I'll provide a few standard realistic fiction characteristics. Realistic fiction most often takes place in the present or recent past. Anything in the future would tend to be science fiction, and anything too far in the past might end up being classified as historical fiction. The setting tends to be places that could be real or are real, and the characters are involved with things that could happen. The conflict and events of the story also need to be things that a reader might face in his/her normal, everyday life. If those characteristics are our working definition of realistic fiction, then "A&P" is a good example of realistic fiction. The story is about young, male store employees ogling some bathing-suit-wearing girls that come into a store located just far enough away from the beach where the girls shouldn't be in swimsuits. Sammy's visions of heroism also fit right in line with how a teenage boy dreams of impressing the cute girl of his dreams. His failure is also realistic. Dreams don't always come true, and snap decisions have consequences. I think the language used enhances the story's realistic fiction as well. Sammy's thoughts jump from topic to topic quite quickly, and he doesn't view his boss or his customers with much respect. He feels that he is somehow better than all of the "sheep" around him, and this is a fairly standard teenager mentality.