imagine self-replicators in a void evolving with the three processes other than natural selection that Myers identifies as important. In the void, there are no environmental constraints; nothing to promote or preserve what Dawkins describes as functional beauty and apparently "designed" complexity, leaving natural selection as the best explanation of those things without claiming that it is the sole cause of evolutionary novelty.
"In a void"? Setting up a completely unrealistic hypothetical situation doesn't prove a point about natural selection, all it does is allow you to deal yourself a winning hand. You've already decided that "functional beauty and apparently designed complexity" are properties that can only be attributed to natural selection, so in your hypothetical setup, it's by definition impossible for such things to evolve.
It looks like you're the one who's misunderstanding what Myers and others are saying. They're not saying natural selection isn't important to evolution, just that other nonselective forces have to be considered too, particularly when they're necessary precursors to selective processes having any truly adaptive effect in many researched instances.
You seem to have missed the main point I picked you up on, which was that there is nothing in the two sentences you quote from Dawkins that isn't compatible with what Myers is saying in the video. Dawkins (and Darwin, were he alive) would readily agree with your last sentence. Variation is essential to Darwin's theory, and three of the four processes which Myers identifies early in the video (mutation, recombination and drift) are the main identified processes that create variation in populations.
Dawkins is merely pointing to natural selection (the fourth process) as being the creator and sustainer of what might be called "functional complexity". Variation is assumed. If you want a realistic example, Dawkins is saying that you won't get the "functional beauty and apparently designed complexity" of eyes in the absence of the selective environmental factor of light, and selection is the only known process that drives the production of and sustains such elaborate systems in variating self-replicators. Myers would certainly agree.
In cave systems completely without light, organisms will not evolve eyes via mutation, recombination and drift, and those species that arrive from lighted environments with eyes will lose them over time due to those processes.
Incidentally, can you think of any characteristics which are at fixation in the phenotype of our own species that could have become so and remained so without the help of selection at some point? Surely, with all this neutral evolution going on, as P.Z. informs us, in small population groups like ours, there must be a long list?