Is this optical illusion the visual equivalent of binaural beats?
Binaural beats result from a difference between the stimulus presented to each ear. The brain tries to integrate them and the perceived low-frequency beat is an artifact of that processing. There are optical illusions that involve presenting distinct, isolated inputs to each eye, and I'd consider those the closest equivalent to binaural beats. 

The apparent motion in the image doesn't rely on binocular vision; you can see that easily by looking at it with one eye closed (in fact, I think that makes it stronger). I'd guess it's probably based on edge detection or lateral inhibition, which don't (I think) have a particularly close analog in sound perception.