What's even more interesting than that is that he resorts to imposing law on people, just like the Pharisees he compares us to.
More helpful than pointing out some slight contradiction in Dawkin's ethics is that at least three of them can be used to show that he acknowledges some form of Natural Law:
In all things, strive to cause no harm.
Treat your fellow human beings, your fellow living things, and the world in general with love, honesty, faithfulness and respect.
Do not overlook evil or shrink from administering justice, but always be ready to forgive wrongdoing freely admitted and honestly regretted.
The biggest question, of course, is why it is bad to "seek to cause harm" or to fail to "treat your fellow human beings... with love, honesty, faithfulness and respect." It cannot be because of social convention (id est, society does not approve of people who fail to treat other human beings with "respect" - whatever that is). This is because he says "Form independent opinions on the basis of your own reason and experience; do not allow yourself to be led blindly by others," presumably, "others" includes society - which is just a macro-level grouping of "others."
If it is not social convention that makes it wrong to fail to respect, love, and be honest with fellow human persons, then maybe it is only an expression of personal preference (i.e. "It is personally very distasteful for me to witness other people being lied to"). This also cannot be Dawkin's belief. If it were, then Dawkins could not present these as rules for others to live; he could only say that he, himself, finds these good rules. Whether a CEO believes that it is good to cheat his workers out of a fair wage (and hence, "disrespect" and be false to them) is not something that Dawkins could comment on.
If it is neither social convention nor personal preference that makes disrespecting and being false to others wrong, then it can only be the result of some external, meta-ethical standard. This means that morality is the same principle as driving; a driver acts legally when he drives at the speed limit, and acts illegally when he drives above it. This means that the legality of his driving is dependent on his acting in accord with the law. The same principle holds for morality; the human person acts morally when he acts in accord with the "Moral Law" which is imbedded in some way into the workings of the universe. Since these principles are meta-ethical, they apply to all persons, everywhere (hence the Nazis at the Numburg Trials were found Guilty - not because they had violated any standing law in Germany at the time, but because they violated the Natural Law).
Since Dawkins must acknowledge some sense of the Natural Law, the question becomes "how did those moral principles 'get there?'" The most reasonable and apparent answer is that a transcendent moral agent exists.