ATwerkinYoshi's set up hinged primarily on a Human Interface Device (HID) called Makey Makey. The simple tool converts basically anything into a keyboard input. In this case, he hooked up bananas to the board so tapping one of the fruits would be interpreted as a button press. He then used an input converter to change those perceived keyboard actions into button presses on a Nintendo Switch Pro controller so it would be recognized by the game. It's a much cheaper set up than buying a Pro controller, though a Pro controller will never get too ripe to play with.
The streamer put the makeshift controller to the test by playing online as Donkey Kong. In an Imgur gallery, he said he expected the experience to go terribly but wound up making things work and rattled off a five-game match streak while streaming the gaming session. ATwerkinYoshi wasn't at as big of a disadvantage as you might imagine; he has a history of creating unconventional controls, including playing The Legend of Zelda: Breath of the Wild with a Guitar Hero controller and Dark Souls 3 with a Dance Dance Revolution Dance Pad.