I'm sorry, those videos mean absolutely nothing. They're yet more propaganda issued by the obsessive barefoot brigade who want to show shoes and farriers as being the spawn of the devil
There's absolutely no scientific backup to show anything at all in those videos. It's like me posting a video of my wonkey legged horse trotting against something with wonderful conformation and claiming the difference is to do with shoes/ no shoes. Erm, no, it's due to wonky legs. Fact is, you just can't compare 2 horses who are completely different and claim that the difference in action is down to the one thing that it suits you to focus on.
It is known that a shod foot will suffer more concussion than unshod when trotting on a hard surface, but without looking at either an individual horse shod and unshod or a huge number of horses which will even out to a reasonable average, it's not possible to quantify that effect. And if you do quantify it, it doesn't suddenly mean that every horse can go barefoot anyway
Thankfully most people - barefoot and non barefoot have far more sense than to fall for it