But it is precisely the "inherited traits" that are so misleading and dishonest. SNPs won't be seen by selection (unless they alter existing information). Genes will be seen by selection, but they are too complex to be built by random processes.
In the weasel example there are no nucleotides. There are single letter changes. Which are seen by the selection method. And each letter change is inherited by the offspring. So it shows precisely what it is meant to show: That inherited traits, with variations, can climb mount improbable if a selection method is employed.
It is nothing to do with 'genes', 'nucleotides' or 'natural selection', other than in the most broadest possible sense.
Dawkins program is akin to me flapping my arms and saying "There, feel the air pressure under your hands? That's how you fly- it's easy."
If Dawkins claimed that his program explained biological evolution by means of natural selection you'd have a point. But he explicitly says it doesn't and he explicitly says it explains something else.