I have no idea who Peter Diamandis/Steven Kotler are but I doubt they had any large effects on the overpopulation of the world.
Regarding "religion": do you think "religions" came up with the concept of having a lot of children?
You don't think it's simply a natural instinct, like in all other animals? And that in a world where few make it to adulthood, people tried to have more children?
This study is in the context of previous assumptions of a U-curved relationship: low equality == high birth rates, medium equality == low birth rates, high equality == high birth rates. That study shows that the last part doesn't seem to be true.
Poverty can probably actually lower birth rates by forcing women into the workforce. If a parent is at home, the marginal cost is a lot lower for another child than it is if people are paying for childcare.
Regarding "religion": do you think "religions" came up with the concept of having a lot of children?
You don't think it's simply a natural instinct, like in all other animals? And that in a world where few make it to adulthood, people tried to have more children?