How does Walter Mitty's character comment on society as a whole?

Walter Mitty is absent-minded. He lives in a world of daydreams. He is not in tune with the modern world in which he actually has to live. Like most absent-minded people he is incompetent to deal with reality and frequently makes mistakes. His absent-mindedness shows itself conspicuously in one part of the story where he is trying to remember one of the things his wife told him to buy. Then when he manages to remember, he says the words out loud. They are "puppy biscuit."
Modern civilization has deprived people of exciting and dangerous lives. Instead they work in offices and bring home paychecks instead of animal carcasses. Many people lose themselves in television and alcohol. Modern man’s frustration explains the popularity of TV shows like Survivor. Walter Mitty is superior to the stereotypical couch potato because Mitty can escape into his own imagination. (There really is not that much difference between the content of his fantasies and the stories shown on television.) Mitty resembles Leopold Bloom in James Joyce's Ulysses. Throughout that novel there is a comical contrast between Bloom, the modern man, and Ulysses, the intrepid hero of Homer's epic poem The Odyssey.
Sigmund Freud dealt with the alienation of modern man in one of his best-known works.
Using the concepts of the superego, the sense of guilt, and the aggressive instinct, Freud formulated the main theme of Civilization and Its Discontents: the ineradicable antagonism between the demands of the individual’s instincts and the restrictions of civilization.

And in The Future of an Illusion, Freud writes:
every individual is virtually an enemy of civilization, though civilization is supposed to be an object of universal human interest. It is remarkable that, little as men are able to exist in isolation, they should nevertheless feel as a heavy burden the sacrifices which civilization expects of them in order to make a communal life possible.
James Thurber was an exceptionally intelligent and well-read man. His humor is more subtle and cerebral than most American humor. He was quite interested in the ideas of Sigmund Freud and other psychologists. In fact, much of Thurber’s own writings and cartoons deal with various aspects of psychopathology.