Here is another detailed criticism.
There are many issues here, such as whether European marriage customs are the result of Catholic teachings of a millennium ago, or Greek and Roman law of two millennia ago.
Obviously it was some combination.
This research came to light when universities did psychology experiments on student subjects, and then found that their results do not apply to the rest of the world.
The research is much more important than that. It goes to the heart of what made modern civilization possible. We need to figure that out, or else we might be inadvertently undermining civilization. It is also important for understanding cultures from other parts of the world.
There is also a nature-nurture issue, and these authors have only scratched the surface.