@Kronous
From the looks of it, it's actually a cork pop gun.
But yeah, the form implies that it's based on an existing real gun.
@themanj
If the form was any indication, the guns of the small arms class of this world are rather advanced (20th century advanced). Early arquebuses were basically just a block of wood with a metal barrel on one side.
The thing with weapons like guns and crossbows is that you can train a peasant for a week and you get yourself an effective enough soldier.
Magic in fantasy is usually reserved for people who study/practice them their entire life - just like with archery, fencing, and martial arts.
Maybe guns are widely used in war, but not by adventurers who are up against monsters with hide and scale as tough as nail. Guns that would have matched the power of magic would have been too heavy to move around.
As for the Gatling Gun, the problem was less about it being hand-cranked, but that it was just another artillery piece. What made its successors usable were the vehicles they were mounted on. It was a matter of doctrine.