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 RN

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.