i don't feel i need to read sam harris's book, as i suspect that one could find more sophisticated or careful or plausible or informed versions of the same sort of argument written by philosophers who have thought about the issue for decades. someone would have to persuade me that sam harris knows enough about ethics of the last 500 years to make his position plausible or push it beyond, i don't know, mill. perhaps i will end up getting sucked in, but i'm too busy reading mencken and figuring out the very nature of the universe: like hegel, i plan to die just before completing the project. oops, almost! anyway i don't really get this summary. the most it appears to argue is that utilitarianism is not incompatible with science. it's "not irrational" to think about improving the welfare or human beings. ok i guess. i was expecting something from evolutionary theory or genealogy that would establish utilitarianism in the face of kantian objections or work out that thing where the actual consequences of any action are incalculable, or explain why we should hang the innocent to prevent more pain etc.
maybe the "argument" is something like this?: each person in fact wants her own welfare (no doubt pushed to do so by evolutionary factors). so all of us should worry about all of us's welfare. mill really really tried to make that 'so' plausible. and yet it is a completely arbitrary inference. at any rate, that evolution makes us want to survive does not entail that we ought to survive. indeed, evolution extinguishes species with great glee, and such extinctions are as important in the evolutionary process as the momentary flourishing of some species. honestly, this kind of argument no more shows that we should take care of one another than that we should take care of mosquitoes.
look it's great that you're a utilitarian. but the notion that your moral theory can be scientifically established is balderdash. and once you have Nature dictating moral principles, you are no atheist.