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.
