If the monkeys' probability distribution function can be transformed to a uniform distribution by a continuous function, the outcomes are equivalent enough for this exercise. (There are probably some discontinous functions that'd also work). So, unless there's some genetic weirdness in monkeys that prevents their ever hitting certain keys, they're adequate RNG engines. But at that point, you're really tweaking the assumptions based on how realistically you think monkeys are portrayed in the thought experiment.

And I don't believe "quantumly random" is a necessary condition here.