When you uncontract doesn't in "Why doesn't it work?" the not moves to "Why does it not work?"
This confuses me even more when I use a longer phrase instead of the pronoun it like below:
Why doesn't this simple code example work?
Why does the word order change when we use a contraction?
You form questions in English by inverting the subject and the verb. For the OP's two sentences, the verbs you use in this inversion are does and doesn't, since you can't separate does and n't.
This simple code does not work.
Why does this simple code not work?This simple code doesn't work.
Why doesn't this simple code work?
*Why does this simple coden't work. (incorrect!)
Historically, this may have developed because in Elizabethan English, both Why does this simple code not work? and Why does not this simple code work? were acceptable word orders. Only the first one is acceptable today.
For an example of both word orders in Elizabethan English, Shakespeare used:
Why should not I then prosecute my right? (A Midsummer Nights Dream, Act I, Scene 1.)
Why should I not now have the like success? (Henry VI, Part III, Act I, Scene 2.)