In Walter Mitty's final daydream, he imagines that he is about to be put to death by a firing squad.
In one sense, this can be seen as an indication that Mitty's fate is to lose his "battle" with his boring, mundane life. He will continue to be dragged on boring shopping excursions by his wife, who will continue to scold him for his forgetfulness.
Mitty's attitude toward the firing squad, however, hints at a different aspect of his fate. Mitty faces the firing squad bravely, refusing to cover his eyes with a handkerchief; he is, at his last moment, "erect and motionless, proud and disdainful." This hints that he will triumph over his boring life, in a sense: he will continue to live an exciting life in his daydreams.
In this sense, Walter Mitty can be seen as an example of an existentialist hero. Existentialism (to make a long story short) is a philosophy that looks at people as being lonely, isolated and overpowered by an uncaring world; the most a person can do is to choose a path that is true to his or her own character and not give in to what someone else has chosen for them. Walter Mitty, in his mild little way, chooses his own path and refuses to give in to the demands of his wife or society at large.