This doesn't seem right to me. The relation between temperature and the kinetic energy of particles in a gas only refers to their chaotic, unordered motion. There is no reason why a directed bulk motion would have a compensatory effect on the random motion that causes the pressure. If you moved a box of air around, the pressure inside wouldn't drop.

I think this is turning cause and effect around. As a parcel of gas moves from a region of high pressure to a region of low pressure, there's constantly a force acting on it, which means it will be accelerated, and thus speed up. But I'll admit that doesn't give an intuition for why blowing air definitely does lower pressure, like in the classic experiment where you blow in between two pieces of paper and they move towards each other because the pressure between them is lower than atmospheric.

The video explains why the pressure in a specific volume decreases if the speed increases. I'm not sure that's correct or not, but it's certainly not what Bernoulli is about. Bernoulli describes what happens along a streamline. It's about how speed and pressure change in space, along a streamline, not about how they change in time, or about how they change in response to outside influences.

the guy spoke too quickly and the whole thing was rushed into a minute