in modern humans. All modern humans, except sub Saharan Africans, have Neanderthal genes. Doesn't sound like genocide to me.
Regarding disease, why couldn't it also be the other way around, that Neanderthals had diseases that Sapiens had not known before? There are Neanderthal genes in modern humans that help us fight against some viral diseases. One unfortunate side effect is that it makes some of us today more likely to develop allergies.
Some studies early in the covid pandemic, done by the Max Planck Institute, indicated that people who did not get sick when tested positive for covid had inherited a particular combination of Neanderthal gene mutations. But some Neanderthal mutations in modern humans made people more vulnerable.
I don't think that it was diseases or deliberate genocide. I suspect that it was a combination of factors. There likely were some fights over territory and resources, between Sapiens and Neanderthal, but also between groups within each of those 2 subspecies that we descend from.
The claim that only Sapiens is genocidally inclined is false. We share a very ancient common ancestor with chimps. Neanderthal, as a hominin, must have that ancient shared ancester, too. Jane Goodall reported on chimp wars of extinction in Africa. One group totally wiped out the other. She also reported cannibalism among chimps. So that level of brutality is not exclusive to Sapiens.
I think that a combination of scarce resources in some places, climate changes affecting resources, intermating, and a continued influx of Sapiens groups from Africa into Europe and Asia all contributed to Neanderthal extinction.
The author's statement that Neanderthal went extinct 40,000 years ago is also not correct. There were still some few Neanderthals in small pockets 15,000 years ago.
This hypothesis about Neanderthal extinction expresses the perspective of the guy who came up with it, but does not fit well with the objective data available at this time.