I think old console games (e.g. for the NES) were like this. You can record the inputs for a speedrun dependant on RNG and replay them on a real console, and so long as the timing is maintained exactly, the RNG outputs will be the same. This has been demonstrated with a tool called TASbot.

I don't think TASbot is a real tool, it's an avatar for any tool assisted speed run using a variety of tools unique to a specific system or game. See https://tas.bot/wiki/Main_Page

A little of column A, a little of column B.

Generally a key generator does not itself watch for mouse-movements, it just gets random noise from the OS. But the OS gets its random noise from a random number generator, and the random number generator needs to be seeded with genuine randomness. Some CPUs provide a hardware RNG, but older CPUs do not, and some OSs do not trust a hardware RNG implemented in opaque, un-auditable microcode, so they get their randomness from things like the difference between the CPU clock and real-time clock[1] or the relative timing of interrupts... such as those caused by mouse-movement or keyboard key presses.

[1]: https://www.finnie.org/software/twuewand/

Yeah, sometimes I am surprised by what I was able to figure out as a kid, with no internet or anyone to really ask how to do things. I had books, but mostly just figured stuff out.

I recreated bastardized versions of so many data types that I learned about much later.