In his mind, Walter imagines that he is the most capable man in the world. In his real life, he is quite incompetent. One might think that, at least occasionally, Walter would try to be competent and successful in his real life, but he doesn't do this. In fact, he purposely tries to avoid succeeding. It is ironic (situational) that he would go to such lengths to avoid success. Consider the scene in which he can't get the chains off his tires. Instead of learning from his mistake or learning from a professional, he chooses to avoid even trying in the future:
The next time, he thought, I'll wear my right arm in a sling; They won't grin at me then. I'll have my right arm in a sling and they'll see I couldn't possibly take the chains off myself.
Walter chooses to be heroic in his mind, but would rather appear like an invalid in his real life.
Note the final line of the story. It ends with "Walter Mitty, the Undefeated, inscrutable to the last." "Inscrutable" means impossible to understand or interpret. The reader tries to determine what makes Walter tick. Has his wife's nagging forced him into the escape of his own imagination? Or has his inattention to his real life caused his wife's nagging? Is Walter happy? Is this retreat of imagined worlds enough for him? Is he miserable? These kinds of unresolved questions are a kind of irony that would best be described as romantic or a type of metafiction. Readers attempt to determine what made Walter into the dreamer that he is. He is "inscrutable" and therefore impossible to understand fully. With this final line, the author calls attention to the unresolved, inscrutable Walter Mitty.
This story might also qualify as Socratic irony. This is feigned ignorance. Socrates would pretend to be ignorant in order to manipulate the person he was having a dialogue with. Perhaps Walter is pretending to be incompetent in his real life in order to live almost exclusively in the much more exciting realm of his dreams.