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The Game Boy Interceptor
there.oughta.be
Today, there is nothing unusual about streaming footage from a Game Boy. Emulators can easily do it and modern Game Boy variants like the Analogue Pocket offer HDMI output that could be captured. There also are some mods to add HDMI out to original Game Boy hardware, so getting a video stream from a Game Boy is a challenge that has long been solved.
The unusual detail about doing it for a Tetris tournament is that the players have to rely on their muscle memory which they trained on their personal Game Boys. Switching them for an unfamiliar modern device or an emulator will significantly impede their ability to play competitively. Also, you can imagine that a tournament that asks each contestant to first mod the hell out of their beloved Game Boys just to stream a video would not be well received.