I'm surprised that it apparently works so well (most of the time, for many games) without knowing the state of inputs, just relying on conditional branching. I would have expected a lot of code to just manipulate registers based on inputs and use those to send different PPU commands.
I wonder if you could achieve 100% parity (and audio) without modification of the console by doing all the emulation in the capture card. Send some pre-built ROM to the console which just reads inputs, sends them back to the "cartridge" and then reads back video output from the emulator.
The same author already made https://there.oughta.be/a/wifi-game-boy-cartridge and https://there.oughta.be/gta5-for-the-game-boy so it seems technically feasible :)
Edit: Ah I see the video stream cartridge runs at 20fps, but gameboy games can run up to 60fps. I suppose that wouldn't work for the original purpose of streaming tournaments.