I had to watch it without audio, I'll have to go back and see if he explained how stereo is encoded in vinyl. One "wall" of the groove is the left audio channel, and the other is the right. The diagonal movements of the stylus perpendicular to the groove walls generate the two audio channel signals, and the movement in the left-and-right direction (in the plane of the record)is just the vector sum of the two diagonal signals. Mono records only have left-and-right movement, which generates two nominally identical diagonal components, which is why old mono records play fine on a stereo turntable.
Cool as it is, its a godawful way to record sound and it always amazes me when people want to bring it back or (ridiculously, IMO) claim that the sound is better in any way, shape, form, or universe. I'll probably always keep my vinyl collection just for grins and amusement, but I sure don't seriously listen to it anymore!
I also have a 1918 Victrola and a small collection of 78 records, which is an equally fascinating (and more different than most people realize) method of recording from vinyl. A fact I learned about 78 records not all that long ago. The styli used are stainless steel points, and the expected life of each stylus was 1 record- you buy them by the hundreds and there's a little tub on the Victrola for new styli and a cup to dispose of the old ones. That's the part I always knew, but the REASON they only last 1 playing is deliberate and kinda clever: The records have abrasive material (various minerals- limestone or silica for example) embedded in the shellac resin so that the record wears the stylus and the stylus won't wear the record. Without the abrasive a steel stylus would last a long time, but the record would get torn up in a few playings. The price paid is that typical, scratchy 78 RPM "hiss" that everyone thinks of. And in fact, playing a 78 RPM record on a diamond-stylus modern turntable will wreck the diamond stylus in short order, too. Back in the heyday of the Victrola, there was a more expensive tungsten tipped stylus(the 'Tungstone' brand stylus) that claimed to be good for 100 records, but most people found that it would start skipping after 1/4 that many.