If both propellers and wings are airfoils, then why do propellers deflect air perpendicularly to the rotor, but wings not?
Don't let wind tunnels fool with your perception of reality. In the real world, it's the wing that moves while the air remains stationary.

Consider a video just like the one you posted, but filmed with a stationary camera. (The one in your video is attached to the wing and moves along with it.) You'd see the folowing scenes:


The field of view is filled with stationary air.
A wing quickly passes through the video from right to left.
The air now moves downward more or less vertically.