Pull-up bar hanged from drywall door-frame
While it is touching the door trim, technically it is not  mounted to or attached to the door trim, or the wall for that matter. One side is pushing against the door trim attached to the jamb and framing behind it and the other side is pushing against its trim  and door jamb and framing,  this creates a situation where leverage is being used to push both sides towards each other.  The weight of the person using it causes the two opposing sides to push harder against each other there by pinning it to the door jamb and wall framing.  

I suppose the risk would be that if the rough opening behind the trim (  The space between the wall framing and the door jamb ) is of a significant gap than the forces pushing against the trim would push the drywall into that void  causing it to crack. 

You could remove the trim from the door and inspect the framing and jamb behind it. You could also replace the trim with a more robust material such as a hardwood  that is wider than your average trim to spread out the force is pushing against the wall. 

Personally I would just try it, any properly constructed door framing should be sufficient and since I can’t read the German Amazon link I can’t know the specific instructions for this unit.