Rather than suggesting that the two works are satires, perhaps consideration should be given to interpreting these works under the genre of farce:
A comic dramatic work using buffoonery and horseplay and typically including crude characterization and ludicrously improbable situations.
For, certainly A Marriage Proposal with Ivan Vassiliyitch Lomov and his continual palpitations, hypochodria,shrieking, and fainting, and with the volatile Stepan Stepanovitch Tschubukov, there is buffoonery and ridiculous situations such as the episode in which Tschubukov and Lomov resort to exaggerated name-calling and Lomov falls into a chair, seemingly dead.
In similarly absurd situations, Mitty daydreams that he is the famous surgeon, Dr. Pritchard-Mitford and the heroic Captain Mitty while Thurber pokes fun of the jargon of military and medical professions with the mock-jargon of the narrative.
Still, there are examples of satire as in "The Secret Life of Walter Mitty," Thurber satirizes the conflicts and neurotic tensions of Mitty as well as the absurdities of modern life with the importance put upon puppy biscuits and getting the snow chains removed. Marriage, too, falls victim to the biting criticism of satire as Mitty refuses to accept responsibility, instead escaping the vicissitudes of life through his daydreaming. And, in Chekhov's A Marriage Proposal, the Russian upperclasses' social custom of arranging marriage for the purpose of acquistion of property becomes a battle over property and manhood, one that will not end with the marriage of Lomov and Natalia.
In both works, then, there are darker themes that lie beneath the humor. Mitty evades responsibility, and Chekov's characters make excuses for their failings, and, like Mitty, stop listening to one another. Both Thurber's short story and Chekhov's A Marriage Proposal do satirize people's failures in dealing with life.