Long story short, progress in population genetics has led to the realization among biologists that there are forces that are more important to evolutionary change than natural selection: non-selective processes like mutation, recombination, and genetic drift. Nevertheless, many writers mislead the public with the notions that natural selection is the sole relevant driver of species evolution, and that all biological traits are by definition adaptations, the product of selective wars between selfish genes in their inexorable drive toward self-perpetuation in the struggle for existence, etc. etc. For example, in The Ancestor's Tale, Richard Dawkins asserted: "Natural selection is all-powerful with respect to those visible changes that affect survival and reproduction. Natural selection is the only explanation we know for the functional beauty and apparently "designed" complexity of living things." If that's not unapologetic adaptationism, I don't know what is.
Well, it appears then that you "don't know what is [unapologetic adaptionism]". The two sentences you quote from Dawkins certainly aren't. There being plenty of neutral evolution is entirely compatible with them. The first sentence actually implies it by defining the type of changes that natural selection would act on. To understand the second, 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.
Either you've misunderstood what Dawkins is saying there, or what Myers is saying in the video, or both.
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?