Dr Chan is LOL cat (repost)

The mechanism of natural selection itself is not random, rather it is variation within the phenotype which is the random process. Variation must be present before natural selection can act; the process which generates variation must drive evolution, and not natural selection itself. Natural selection, rather than being random, is a perfectly explainable correspondence between characteristic and environment.

Variation in phenotype is driven by random genetic mutation. The proximate mechanism of natural selection is fit between organism and environment. This is indeed perfectly explainable, but the underlying process that drives evolution -- as you say, a necessary condition -- is random mutation. It depends on how one delimits the causal chain of events whether one includes random variation in the mechanism of natural selection. You are probably right to say that the mechanism is not (entirely) random, but the driving force is randomness. This is why it does not makes sense, strictly speaking, to talk of "progress" (or design) in evolution.