You're just proving his points Lasse. 1. Your video proves that the FE guy who made it is disingenuous, as he said, and 2. Your video actually proves that the Earth is round.

1
The guy who made that video must have watched the original source material (he even gives it up as a source in the title and description). There, everyone can see that they use a fish-eye lens and that the Earth appears round whenever the horizon is at the centre like below. (The full playlist of the original material can be found here)

So why would he, on purpose, cheery pick the part of the video where the horizon is below the centre of the frame and thus distorted the way he wants it to be? (PS, if you use a ruler at different points in the video you linked, you can even spot a slight upwards curve, proving its distortion). This just goes to show what @amaterasusolar said, that the people who make these videos are disingenuous and dishonest. Or just desperate to believe what they want to believe.

2
Now that we know the video is shot with a fish-eye lens (which is normaI for high altitude footage) we can take that into account when looking at the image. If you really care about the truth, then you'll do some research into how fish-eye lenses work. Long story short: The centre of a picture taken with such a lens remains mostly the same. The lower parts at the centre concave more down, while the upper centre parts concave more up. If the Earth was indeed round, we would therefore expect it to appear flat when the horizon is slightly below the centre. Oh wait, it is EXACTLY that in your video! Your video displays the Earth just how we would expect it to be if curvature did exist.

So let's take a screen shot of when the horizon actually is at the centre:

There you go!

Please find me ONE video where the ENTIRE flight is captured where it shows no curvature also when the horizon is at the CENTRE of the image. Only then will you have any form of evidence to back your claim.