Running correctly is an excellent way to instill good movement patterns. Having watched the video above numerous times, I wouldn’t call these kids good runners. A couple of them are plum goofy. But they all run on the balls of their feet and that is preferable to heel striking which is a fairly standard adult running pattern.
Walking is falling and running is falling oh so slightly faster. One of the joys of running barefoot is that it is pretty uncomfortable to strike your heel without the protection of a shoe (though some people still manage to pull it off) so people often find their way towards a decent form. But I spend a good amount of time in Prospect Park watching walkers and runners of all stripes and I have seen plenty of barefoot runners who are doing themselves no service.
Running barefoot is not the only way to run but it can be very helpful in understanding the stresses we put on our body that can often be hidden by shoes. The less support we receive from footwear the better it is from my perspective.
Little kids move naturally. Watch any child at a playground and I will almost guarantee that they will lean forward before they start to run. At the same time my kids have already put some terrible patterns into the way they walk. They are the product of two loose and open hipped people so they both hyperextend like crazy when standing and walking. The minute they are running barefoot in either karate or on the playground they move beautifully.