A biased sequence can still be random in some senses. The comment to which you reply is correct: all pseudo-random sequences are deterministic, because that's what the term means: a pseudo-random sequence is an algorithmically produced sequence which passes whatever your favourite statistical tests for randonmess are.
You're correct that non-determinism and randomness are different: in mathematical modelling of systems, a "non-deterministic" choice is one that is not made by the system of interest, but by its environment: e.g. a vending machine has a non-deterministic choice between receiving a "tea" button press and a "coffee" button press, as which one happens depends on the environment (the user). In theory of computation, a non-deterministic algorithm really means one where all possible choices are explored in parallel; or alternatively, you can take a lucky guess as to which choices you should make.
"Random" refers either to statistical properties of a sequence - and such a sequence can be a determined thing, just not determined by any computable function - or to a primitive notion of probability. In the probabilistic case, biased outputs are included: for example, if you generate a sequence of bits every second by seeing whether an atom of uranium has decayed in that second, that sequence is, as far as we know, truly random in every probabilistic sense of "random". The ratio of zeroes to ones, however, depends on how much uranium you have. In the algorithmic case, a biased sequence is not random becase it can be compressed - if the string has ten times as many zeroes as ones, then you can trivially compress it by coding sequences of zeroes, and you'll win - but it can still be a random sequence in the probabilistic sense.
Cryptographers want sequences that are random in both senses.