I don't think it's purely genetic either, but I do think there is a part that's genetic, the elements are restricted by nation, but if two people from different nations mix they can have children that posess different types of bending (like Aang and katara's children) so I do think some part is genetic. Also the avatar is something entirely different, I'll ask the person who made the vid to explain how that works with genetics, hehehe
ok I watched the video, I think it sucked, though I don't think I'd be happy with any genetic explanation of bending in the series. Why? Because the Avatar exists. The Avatar is proof that bending is not genetics related at all, but is entirely a spiritual/magical matter in the series. If it was genetic, then there is no way the Avatar, who can bend in all 4 (5) elements, would have ever existed prior to the mixing of nations.
Yes, certain elements are restricted to certain nations, but that seems to be a decision of the spirits, rather than a matter of blood (though I guess mixing was always restricted, so I can't be too sure on this). They gave humans the knowledge and ability. If it was genetic, such a transfer of knowledge would be unnecessary. We know the stories aren't just myth and legend, since both Aang and Toph were taught by animals/spirits to bend.
I'm tired so I'm not sure how much of it made sense, so to summarise
1. Bending is entirely a spiritual matter, since the Avatar exists
2. Designation of which nations can bend what is left to the spirits/spirit world, who controls such matters.