Eugenics has been shown time and time again to be junk/non science. This is like criticizing a dermatology study for not "controlling" for the possibility of lizard people.
GP isn't referring to eugenics. GP is pointing out that there may be heritable traits that lead one to be more successful in a PhD program. This could be grit, determination, ability to focus, or ability to recognize patterns. It would be surprising if there were no heritable traits that affected success in PhD programs.
GPs comment is no more eugenicist than someone pointing out that children of NBA players are more likely to play in the NBA because height is somewhat heritable.
Or it could be that children of PhDs come from an environment where they know what’s required to get a PhD. Neither of my parents had bachelor’s degrees. I had no idea that any PhD worth its salt would be something that the PhD student was paid to attend rather than would pay to attend.
And as an aside, my cousin’s husband has a PhD and yet none of his kids have graduate degrees, while in my family, out of three brothers, there’s a DVM, and MS and me with a MS and MFA.
No one is debating whether there are environmental factors. Surely there are. The point is that there are also likely heritable factors. These cannot be erased. And without measuring them, we don't know how much of a "problem" it is that many professors have PhD parents.
Possibly, and that's what the whole video is about. The point is that we don't know how much of the difference is behavioral or related to wealth if we don't even try to consider the possible effects of heritability.
GPs comment is no more eugenicist than someone pointing out that children of NBA players are more likely to play in the NBA because height is somewhat heritable.