Inscrutable means hard to understand or interpret. For the reader, Walter is not inscrutable. We know why he retreats into his imagination. He is not the stereotypical masculine man, not one who gets things done; and this irks his wife to no end. She is overbearing and a major factor in Walter's continuing practice of seeking solace in his own imagination, but she is also stuck with a man (Walter) who continues to lose focus in the real world in order to focus on his own daydreams.
So, the reader does have a pretty good idea why Walter acts the way he does. However, it does take a bit more thought into why Walter has become this way. One argument that has been made is that Walter lives in a modern time and his career and lifestyle have made it conducive for him to become bored, unchallenged; therefore, he resorts to daydreaming in order to compensate for his boring life. This is a common theme with modern man (and women in other texts) whose instincts command action (hunting, etc.) but living in a modern, civilized world, modern man is restricted to mundane desk jobs, grocery shopping, and so on. So, all in all, Mitty is not inscrutable to the reader.
However, why would Thurber end the story with:
Then, with that faint, fleeting smile playing about his lips, he faced the firing squad; erect and motionless, proud and disdainful, Walter Mitty, the Undefeated, inscrutable to the last.
In this daydream, Walter is inscrutable to the firing squad. They can not fathom why he is so confident and proud. Either he is unafraid of death or he knows that he will escape from this predicament as well, unbeknownst to his captors. Also, in the real world, Walter is inscrutable to his wife. She is always confounded about Walter's absent-minded behavior. Even others around Walter (the parking lot attendant, the woman who overhears him saying "puppy biscuit") don't understand what Walter is thinking/doing/saying.
So, to the reader, Walter is not inscrutable. But to the characters in the story and the characters of his own imagination (who do not know of his incredible abilities), Walter is inscrutable. We get him; they do not.