Edit: Ben explains this in the video; there are actually two axes of movement, sort of diagonal to the plane of the disk, each of which encodes one channel of a two-channel stereo recording. I'm sure many LP fans already know this, but it's a revelation to me.
BTW, Ben Krasnow is a heck of a guy. A true polymath and a generous teacher.
These other channels were recorded with FM (frequency modulation) on top of a 30 kHz carrier. The 30 kHz carrier was just high enough to isolate the quad channels from the 0-15 kHz ordinary left/right stereo channels.
And then, the FM portion, centered around 30 kHz, was added to the regular baseband audio signal (0-15 kHz), and all encoded into the diagonal displacements you mention in your comment.
It always baffled me that it also worked on an ordinary stereo - and I sometimes wondered if I had been had.
We now have the tech to encode many channels in one MP4 stream, but don't we don't bother and just stick to 2 for sound. What does that tell us about the future of 3D TV and 360 degree video? Perhaps more of us will stick to the old tin boxes.
Good multi-channel sound immerses you in an experience, and is worth a significantly smaller screen as a trade-off, if you have to make it.