You are 100% mistaken that this implies we had a good definition of random sequences before Knuth. In the article you link, they discuss the uniform distribution, but any distribution (and the modern notion of probability in general) absolutely depends on a mathematically precise notion of random sequences.
If you don't believe me, read the chapter. Early probability theorists (e.g., von Mises, Kolmogorov) literally started thinking about randomness in order to define probability.
EDIT: And, I don't suppose it's worth pointing out that pseudorandomness is not at all the same thing as randomness. The fact that you seem to use them interchangeably is not a good sign IMHO.
If you don't believe me, read the chapter. Early probability theorists (e.g., von Mises, Kolmogorov) literally started thinking about randomness in order to define probability.
EDIT: And, I don't suppose it's worth pointing out that pseudorandomness is not at all the same thing as randomness. The fact that you seem to use them interchangeably is not a good sign IMHO.
EDIT 2: Why the unexplained downvote, HN? :(