Good video, but it seems to somewhat conflate FM synths (e.g. Yamaha YM3812, YM2610, YM2151) with primitive envelope+counter-based PSGs (e.g. General Instrument AY-3-8910/Yamaha YM2149, Ricoh/Nintendo 2A03, Texas Instruments SN76489). I'd argue that the character of these two classes is substantially different. The PSGs are much more built around pure waveforms (for certain interpretations of "pure waveforms" that include pseudorandom noise), while the FM synths tend to be built around sets of parameters that produce sounds almost, but not quite, entirely unlike traditional musical instruments.

Another interesting bit of trivia is that the Yamaha "FM" synth chips were actually based on phase modulation (PM) rather than frequency modulation (FM). The abstract math can be transformed back and forth between the two, but the PM formulation accumulates less error when directly expressed in digital hardware.

The Commodore SID is arguably in a class of its own and probably can't be fully explained without some kind of textbook-length exegesis.

edited to add: samples to try to demonstrate what the heck I'm blabbing about with the difference between PSG and FM:

PSG: https://www.youtube.com/watch?v=uyMKWJ5e1kg The Legend of Zelda - Main Theme (Koji Kondo; 2A03)

FM: https://www.youtube.com/watch?v=JWPNxSD9YNY - The Revenge of Shinobi: The Shinobi (Yuzo Koshiro; YM2612)