That is a supported position, and that is likely the sole purpose why he's sitting like that. Notice as well that his elbow is not resting directly on his knee but slightly behind it so you do not obtain a hard on hard surface contact.
When 2 hard surfaces contact each other vibrations can easily be transmitted from one object to the other, if you have a soft surface inbetween those vibrations dampen out pretty much allowing for a more steady shot.
But the whole point of having two contact surfaces is to eliminate the influence of muscle fatigue and sway due to lack of stability in the hands.
Just propping your elbow on the ground isn't going to eliminate that, and it isn't going to reduce sway as considerably as if you were resting it on an object.
Vibrations would occur between shots, and would only affect the time required to stabilize the object. You can prop a rifle or any object for that matter in a stable position on a rigid object. For instance, if I set a crate on top of a crate, the crate will not wobble and less so if I touch it than if it were on a bean bag chair.