[darkmighty]

Your definition of "randomness" is interesting (but classifying it as a problem is misleading). Of course, if you don't have profound knowledge/skill of a game and you're not able to evaluate moves, their outcome will seem random just because you're ignorant of them. That's exactly what differentiates good and bad players! If the game were not random for newcomers and they could predict the outcome of every move, they would win or lose solely based on starting conditions (i.e. the game becomes perfect play tic-tac-toe).

[j_h_s]

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.

[darkmighty]

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.