[vamin]

I'll propose a theory: very loud, low frequency sounds actually create small vibrations in your eyes, and most brains have learned to pipe this sensory input to the auditory cortex. So, the shake in the GIF triggers a "sound" through your eyes.

[pb060]

It could also be the tensor tympani muscle tightening in response to a visual event that would normally be accompanied by an extremely loud noise.

[Flenser]

That's also my theory. I can do it at-will by tensing my jaw muscles and I hear a "thudding" vibration sound. (Although I wouldn't have known what the name of the muscle is until your post.)

[pb060]

I can't do it at will but few times I was waken up by the "sound" of it vibrating, quite a scary experience!