There are several things I noticed in the video. First the Bebop2 camera does not have gimbals so the video stabilizing is done all digitally. The camera actually has a much higher resolution then what is recorded, this helps with stabilizing the video during flight. In a way this is a better system because there are less moving parts, less things to go wrong. Under normal flying, this works well. It is normal to see black bars on the sides when its trying to compensate
Video quality will be degraded when flying in sports mode, the drone cannot compensate fast enough to keep the video stable, I would imaging the same thing with a drone with gimbals. That is why they have a setting for video mode and sports mode.
I also noticed that it was cloudy out when you took the video. The Bebop2 video capture degrades when the light is poor. If it was sunny out, the video quality would be better. Its just a limitation of the camera.
In this video, I switched from video to sports mode. (the speed goes from 15mph to 34mph) and you will notice "jello" effects in the video. This was also taken on a sunny day and I wasn't doing any fast turns.
I was testing a booster mod kit by flying as far out as I could.