That's because the camera has a different FOV than your eye. Which camera's were used in this, look up the FOV.
Ignorance of camera technology is the root cause of your misunderstanding.
All of the high altitude balloon footage shows it to be flat. This one is swinging too much. There is footage from 123k and 109k where it is calm. NASA, Red Bull etc use camera's with a fish eye lens. Even the red bull guy had a regular camera inside the cabin that looking out the door show it to be flat while the outside camera has a fake curve.
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