Actually it is being pulled by one link at a time. The other links are just sitting idly on the ring. Think of the distance the chain has to move when you rotate the crank by a small fixed amount - say 10 degrees. That 10 degree rotation pulls a greater length of chain when the oval is standing on end than the same angular rotation does when the oval is horizontal. For small angles of theta:
Chain distance = sin(theta) x radius at that point of the oval (i.e. distance from the BB axis to the edge of the chain ring where the chain first touches it)

Try it with a chain ring that has a pronounced oval shape such as the one illustrated or the ones made by Roger Durham many years ago and the change in effective gear ratio is immediately obvious as the cranks speed up when the oval is horizontal and slow down when it's vertical. OTOH, I never really felt the effect with Shimano's Biopace. Whether that has any benefits is another question. I never rode any significant distance with oval rings - just tried out a friend's bike with them. Certainly felt different but not really better.