Just as karate has evolved over time, we should expect the teaching of karate to evolve as well, and in the West, there are lots of schools without a lot of formality.
I believe respect is important in any educational setting. And it is also important between younger students and their elders. And for that reason, I do find some value in the Japanese/Okinawa hierarchical approach to karate instruction.
I also believe that different cultures have their norms of behavior in educational settings. And just because there may be a desire to learn the movements of karate, shouldn't mean we should always expect the whole Japanese/Okinawan teaching to be adopted as well.
While others will have very different opinions on this, I don't happen to like much of the hierarchical etiquette in many traditional karate schools in the West. I have seen SOOOO many schools where this requirement for "respect" is taken to absurd lengths, where the sensei demands or is given near god-like cult status.
So for these, and other reasons, I have rejected a whole lot of the trappings of Japanese etiquette in my dojo.
My observation of the dojo on the youtube clip, led me to believe that the kids were having a lot of fun. This, to me, is one of the key elements of a successful school that wants to teach lots of kids. It's got to be fun, because if it isn't, the kids aren't going to want to be there. And those kids entering the dojo, commiserating with their fallen comrade, or applauding the quite awesomely timed Unsu kata, looked like they really wanted to be there.
I do recognize the drawbacks of cutting back on all the formality. I teach college students, and I really want them to enjoy their time in my dojo, so, for example, I am not insistent that people don't communicate in my class, except when I am demonstrating something.
But I have found that groups of friends will chatter during warmups, especially stretching. And when that happens, I find that's just the best time for the class to drop for 100 crunches, followed immediately by 50 pushups, and then perhaps some more crunches or some other tiring drill.
I find that this always seems to get the message across that the talkers had crossed the boundary of quite chatter into disrespectful rudeness.