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Regarding the chip just being a duplicate destination of the inputs, I wonder how many games are deterministic enough for this to be possible. I feel like a lot of effort put into modern multiplayer games is ensuring determinism where if you capture the set of user inputs, it's guaranteed to be replayed into the same game, but that perviously a lot of race conditions or randoms() would make that not true.

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The Game Boy is very deterministic. It had no internal source of randomness.

if i remember correctly, the rng on tetris on the gameboy is terrible, and is quite predictable. https://tetrisconcept.net/threads/randomizer-theory.512/page... has some more info about it. Im not familiar with with how some of the prng algorithms are seeded, but maybe on tetris, the hardware responsible is part of the cartridge and then can be intercepted. just a thought tho

I would be very surprised if the Gameboy, like practically any 8 bit CPU of that era, had any dedicated instructions or hardware for RNG.

So it's a software RNG, and the user input is pretty much the only "random" thing coming in from outside. This is very common for games. It still is: Games like Civilization often let you specify the seed to initialize their software RNG with, so you or someone else can replay the exact same game.

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