Why is the deg needed in this sentence? Is ønsker a reflexive verb? Does the sentence make any sense without it?
The reflexivity emphasizes that it's a wish for oneself. It can be dropped, but that sounds archaic.
I think the sentence can be better translated as "What do you wish for yourself?"
I agree, the sentence "What do you wish?" sounds awkward in English in this context, it should be "What do you wish for?", in order to imply the wish is for oneself.