I've looked at the "Weapons Law of 1996" (in german), specifically ยง2 (2), which states that regulations of firearms also extend to the barrel, the drum and the breech.
I am uncertain if this also extends to magazines, given that I can simply go into a gunstore and buy a magazine for a category B weapon without any sort of validation.
In relation to that: Would I be able to buy a magazine online and have it shipped to me?
After some more research, I found several german retailers like Frankonia and Brownells, which do ship firearm magazines to Austria.
My reasoning is as follows: If they were regulated in any way, they would either be confiscated or sent back to the store. In either way, the customers would get in contact with the store, and the store would stop shipping magazines to Austria.
Since I was unable to find a german store which specifically mentioned that they would not ship to Austria, I am going to assume that they are not regulated and can be purchased freely.