In the short story(,) "The Secret Life of Walter Mitty"...

I am a British English user, and I would not use a comma there.

I would've dropped the one after "Mitty"

One of those two (the one after "story" and the one after "Mitty') has to go. In my opinion it really wouldn't matter much which one.

Keep one, but not both.

I've changed my mind. Looking at it more closely, the one you have in parentheses is the prime candidate for elimination.

What I actually started out to say was that you could remove both. I don't see either as necessary, but I wouldn't say the one after "Mitty" is "wrong," either.