Neat work, but their method of improving the audio quality is not very good. They could get much better results by looking at the magnitude spectrum of the source audio, lowpass filtering with a cutoff chosen to keep 95% (if possible) of the energy (likely 1-2 kHz) then downsampling to nyquist. 4 kSamp/s @ 4 bits per sample would sound much better than his method, and it wouldn’t take extra fancy software tricks. The driver/speaker on a gameboy isn’t going to have a very controlled lowpass filter, and it’s behavior is also unknown. Delta-sigma is heavily reliant on the output lowpass filter.
https://www.youtube.com/watch?v=fooSxCuWvZ4