Screwed.

The two Puzzlanian screws are unusual because they are threaded backwards- someone accustomed to normal screws would have difficulty screwing or unscrewing them, because the direction of rotation is backwards.

However this feature does not affect the solution- the screws neither move closer nor further apart. Looked at another way, while one screw tries to climb the other, the other climbs away at any equal rate.

So the screws do not move relative to each other, do they move left or right relative to their environment? Unless the mechanism rotating them also pushes in one direction or the other, no.