Or it was just bad luck for them. Yet, the real problem isn't explaining how we might have won out as the prominent species, its explaining how they could have gone extinct globally, in such a short time. Remember, modern humans were hardly filling up the land masses, and mainly abandoned harsh climates, like the ones that Neanderthals survived in for a few hundred thousand years. So where did they go. Even intentional or untentional genocide can't explain full extinction, when modern humans occupied such a small percentage of the land mass.
Neanderthals were never global. Their range was limited to Europe, which right there is a sign of their cognitive limitations by comparison to modern humans.
I think the wave of human settlers appearing in the Middle East and Europe before the Ice Age Maximum of about 35,000 years ago brought hunting pressure and perhaps warfare, as stated by the author, but disease, if carried over to a previously isolated population of humans, like it did to the American Indian, could have easily wiped out our Neanderthal cousins.