I would say this story serves as an example of person vs. society (though in this context, one might also see elements of person vs. self).
"The Story of an Hour" opens with Louise Mallard being alerted to the news of her husband's death (news that will be shown to be false at the end of story). After hearing this news, she falls into grief and retreats into her room. As the story continues, it follows the evolution of Louise Mallard's emotions in the aftermath of this moment. In this, it certainly contains a strong element of person vs. self (and should be viewed in such a lens).
At the same time, however, this story ultimately centers around an epiphany on Mrs. Mallard's part that stems from a far deeper struggle against the society in which she resides. It is this epiphany that ultimately empowers her, giving rise to what Kate Chopin refers to, within the story itself, as "a monstrous joy." Ultimately, widowhood means the realization of personal agency. For the first time, Louise Mallard belongs to herself.
Thus, her husband's death has set her free. Note, however, that she does not seem to harbor any particular resentment to her husband himself. Indeed, consider how Kate Chopin writes the following about him:
She knew that she would weep again when she saw the kind, tender hands folded in death; the face that had never looked save with love upon her, fixed and gray and dead.
This, then, is not a story shaped by person vs. person conflict. Rather, her problem is the sexist and chauvinistic foundations that lie within the society she inhabits. It is these assumptions and expectations that she is struggling to overcome.