[Flenser]

I suspect it's due to people tensing their lower jaw in anticipation of a loud sound. I can do this at-will, and I hear something that I would describe in similar terms. I also triggered/heard it the first time I watched the animation (and I don't think I did it deliberately, although I was expecting it to happen).

My theory is that it's due to the jaw muscles vibrating when they tense, so an entirely physical sound conducted through the jaw/skull; rather than a neurological sound. I expect if you stuck a sensitive enough microphone in my ear, it would be audible.

[koliber]

It may not even be tensing of your jaw.

https://en.wikipedia.org/wiki/Acoustic_reflex

Maybe this GIF is causing this reflex to fire. In the absence of the loud anticipated sound, your brain may be interpreting the flexing itself as a sound.

[Flenser]

Yes. I expect that's it. I think the jaw tensing may be a side-effect of how I get that to happen.