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Old games put the P in PRNG. Often, the technical limitations caused them to very roughly approximate randomness, for example a function that used the last n button presses plus the countdown timer as a seed. If your game has to run in under a kilobyte of memory, that n value might be a byte, or less (such as four bits, 2^4)

Some games were worse, far worse. Doom used a list of 256 random numbers that it looped through.

Pokemon is another game where the RNG function is extensively mapped, and even used in combination with bugs to generate Mew events, something that should never ever happen.

You see a lot of TAS of old games, especially popular ones, that abuse the RNG generator where feasible.

If the result from the RNG is not actually perfectly random, and is actually partially determined by e.g. controller input, then even if the function is discontinuous there may be a continuous function that approximates it closely enough to be useful.

Old games have such predictable RNG that humans can manipulate them in non-TAS runs. See the run for Final Fantasy 1 for a good example.