How does he do that?

This is described in the document (sections of interest are "Emulator Choice" and "SpongeBob video sequence"). To make it very brief, what's happening is that Pokémon Yellow is acting as an interpreter for commands that get sent to an engine that renders tiles+sounds. These commands are sent through the key inputs. A specific emulator that polls the keys at a subframe rate (very very subframe indeed - thousands of inputs per frame) is used so a lot of data, such as video, can be sent.

In a way, you can imagine what you're seeing not as a GameBoy Color game being played, but as a video being streamed to a GameBoy Color video player using a specific codec optimized for the GameBoy hardware.

Great response - I think what a lot of people miss in these pokemon code execution setups is that the inputs are being streamed to the console _really_ fast

I'm assuming that the parent comment was referencing the specific Spongebob quote in the video, rather than asking for a serious explanation.