Chess isn't random, it's chaotic. Where randomness is unpredictable, chaos is deterministic but so computationally complex that it can't practically be solved. Chess is the art of navigating that chaos.
That definition of randomness is actually fine (randomness as ignorance), it's consistent, and the most often used definition actually. For example, take the Monty Hall problem: it doesn't matter what process Monty actually uses to choose doors, all that matter is you're ignorant of it (so you choose the uniform prior).
In fact I don't think many processes in nature are truly random (quantum phenomena have to have a large effect and you need to choose a no-hidden-variable theory), but it doesn't really matter. It's just a model.
In fact I don't think many processes in nature are truly random (quantum phenomena have to have a large effect and you need to choose a no-hidden-variable theory), but it doesn't really matter. It's just a model.