After watching the video, yes the video maker is indeed misinformed about noise shaping but his heart is in the right place. He is explaining how the goal of the process is to have “quantization noise” (in his case he is confusing quantization noise with added noise) be softer (less power) at higher frequencies and more power at lower ones.
As for the “quantization error noise” shaping (as a math major ) I understand that in a dithering process, quantization error from dithering of the previous sample can be added (after processing the error using a finite impulse filter) back to the next sample like a feedback loop. And result is the same, the error gets shaped .
With noise shaping in the dithering process, we lower the noise floor in sensitive areas of the band.
Certain plugins allow you to choose whether or not you wish to shape the noise caused by dithering, and they allow different methods (filters) for shaping that noise as well.
and yes this is hugely off-topic from the original topic lol