How could “The Story of an Hour” by Kate Chopin be described as realistic fiction?

Works of literary realism aim to represent reality in a truthful way. Realist writers often write about everyday people doing everyday things, going about their lives in a way that is meant to feel realistic and honest. They tend to stay away from romanticizing topics like, for example, marriage.
In this story, Chopin certainly avoids romanticizing Mrs. Mallard's marriage or her life as a married woman. A train accident is believed to have killed her husband, Brently Mallard, and rather than fall apart with grief, lamenting that her other half is now lost to her forever, Louise Mallard instead secretly rejoices in the freedom she now anticipates having as a widow.
Marriage is presented as a confining institution that results in compromises for the wife, which are uncomfortable at best and repressive at worst. Chopin does not attempt to sugarcoat Louise Mallard's feelings of joy. She feels some remorse because she knows that her husband loved her and she loved him too, at least sometimes; but her freedom and independence is worth more to her than that love ever was. Her response to his death is somewhat shocking and certainly not romanticized; it is presented realistically, even if that means our heroine is flawed and human.