The sounds seem to mostly be modulated sines with limited timbral variety? I'm not sure how https://youtu.be/NYX_eeNVIEU?t=179 got harmonic series out of the building blocks.
If this doesn't make sense it's entirely my fault for explaining it poorly -- I really want to write this up properly with some diagrams because it's a surprising thing and quite interesting, at least to me.
(BTW that demo has other things going on like mic isotropy and analog oscillators attached to vibrate two of the masses, so my spring tangent is not the only thing producing harmonics.)