Even though Mr. Mallard seems like a perfectly nice guy, the fact is, right after seeing him alive again, his wife dies. And, even if that never happened, the fact that she was so glad to be separated from him is pretty troubling. It wouldn't be too much of a stretch to say that his presence in her line of vision is what kills her. In that way, Mr. Mallard is totally an antagonist – how else would you describe someone who's killed the protagonist, or severely endangered her? What Mr. Mallard feels about his wife doesn't even matter in this context, and his actions don't matter either, because the very thought and sight of him is deathly to the heroine.
Really, you could argue that death is always going to be the ultimate antagonist, waiting in the wings to carry off every single character at the end of his or her story, if not the end of the story the author's telling. Plus, your every-day, garden variety antagonist – the kind who wants to bring down or destroy the protagonist – frequently relies on death as a threat or an optimal plan for getting rid of the protagonist. The idea of death accompanies many antagonists, and is often a threat for protagonists, so it's only fitting that in this story death steps forward as an antagonist in and of itself. From sentence one, death is something the protagonist, Mrs. Mallard, has to be concerned about. But in trying to avoid her own death, while dealing with her husband's, Mrs. Mallard doesn't realize how close death is staying, and how easy it will be to fall into its arms.