I can't read most of the words because the video is so blurry.
My first guess from just listening is this sort of sounds like an oscillator modulated by a sawtooth. But there's a lot going on. The demo shows more than one knob being changed at the same time, which really makes this difficult to figure out just by watching & listening (without being able to read the words). Sorry, I just can't tell from this video how this really works or what you'd do with the audio library to get a similar effect. But I'd suggest starting with wiring up several pots to analog pins and experiment with the modulator oscillator and adjust the frequency & amplitude of the modulating waveforms.