Short answer, an autococker (assuming it doesn't have an electronic grip with full auto, psp, etc.) is semi-auto.
But, and better get your heads straight cuz it's gunna get technical up in here, it operates differently from your typical semi auto. All autocockers, as well as pumps, are closed closed bolt guns. Meaning the bolt starts in the forward position. When the trigger is pulled, it firsts fire's then cocks back. When the trigger is released, the bolt moves to the forward position while loading a ball into the barrel.
So the action when the trigger is pulled is fire, bolt back, bolt forward/load ball. While with open bolt guns ( practically all non pump guns) operate like this: bolt forward/load ball, fire, bolt back.
Not pulling the trigger back far enough can lead to short stroking where the gun doesn't recock. Then there's getting the timeing right which involves adjusting the points on the trigger to fire and recock to work in sync with the 3-way, cocking rod, etc. It can get pretty technical and confusing but it's simple once you understand it.
Autocockers used to be called snipers before the pneumatics and when they had pump kits. Essentially, the pneumatics do the same action that you would when you had to load another ball and recock the gun. Hence the name autococker. Of course not to many people call them snipers now because of what it implies.