The Witch-King can fight a wizard for the same reason elves can fight and kill the greatest dragons and balrogs themselves. Binding creatures of spirit into physical form both weakens them and makes them vulnerable to other creatures built of both natures. If anything, as a wraith, he has an advantage in Tolkien rules.

That the Witch King is the equal of a balrog/Maia is not a stretch… Gandalf bring afraid of him even if he is a threat is the stretch, but I’d also argue that’s not being shown in the scene.

Balrog who is also a Maia*

Maiar is plural