It isn't always "Hang the teacher" time for things like this. Exercise as punishment from a PE teacher is pretty normal. What happened to this girl isn't a common occurrence. He/she may have told this girl a few times before and she just didn't like playing badminton.
We used to stand at the front gate to greet the kids and hand out punishment for all sorts of nonconformity discrepancies, no socks, wrong socks, wrong shoes, wrong or incomplete uniforms, hair, nails, etc.
Sent 1 girl off to collect 8 pieces of litter as punishment - when she thought she was far enough away that we couldn't see, she took a sheet of paper and tore it into 8 pieces and came back smiling. I gave her points for creativity.