[masraum]

Based on the photos, that does look like it would be trapped. If you unscrew the seat, and push the back up, does the back of the seat hit the bottom of the seat-back so that you can't get the seat higher than the seat-back? It looks like that might be the case. But based on the shapes (and not having access to the chair) that seems like the only way that the seat would come out.

If you lift the back of the seat, can you then rotate the seat? By lifting the seat, it should pull the front of the seat away from the arms, and once's that's happened (if it's enough) then maybe you could rotate the front of the seat right or left under the arm on one side enough to then rotate the back of the seat. No idea if that would help. I'm guessing that the seat was installed after the frame was put together, so it seems like there has to be a way to get it out without disassembling the frame.