The speaker seems far more impassioned by the ends than the means he used to get there, which is a huge red flag. He speaks delicately about a foundation for universal morality, but forcefully about certain behaviors which are more or less unique to the middle east. That's not to say that he's wrong about his conclusions, but it seems likely that he started with the conclusions and built a logical structure to support them. Why even mention burqas? Why not wealth disparity? Or access to food, or healthcare?
It's a bit like specifying a system architecture for general purpose computing and then saying "...and we could use it to play Tron!" It doesn't mean the architecture is a bad (or good) design, just that one should be wary that the design may be biased toward playing Tron, since that was clearly the goal.
At any rate, he doesn't really provide a clear, logical progression from "there are facts" to "ergo, ethical behavior." The terms are too nebulous, and the goals too ambiguous. For example, he says that "whatever cultural variation there is in how human beings flourish can, at least in principle, be understood in the context of a maturing science of the mind." Well, is that human beings in the individual, or the collective? When there's a conflict between individual flourishing and the collective flourishing, which outweighs the other? And how do we define "flourish," anyway? These anbiguities are all symptomatic of trying to create a framework to support a conclusion rather than the other way around.
Honestly, if humans were capable of defining universal morality, I believe we would have done it by now, or at least have some coherent foundation. It's not something that requires a technological solution; it's applied logic, like algebra, which has been around for thousands of years. Even calculus has been around since the 1600s. Our theory of everything in physics is more complete than any theory of universal morality, and that's saying something. There are simply too many variables. What if infanticide prevented the rise of someone worse than Hitler? Hell, what if Hitler prevented the rise of someone worse than Hitler?? There's just no way to know.