Humm... First article... I am not convinced. Genetics has proved that Neanderthals and Cro-Magnon mixed up to a level, rather than the former being extinct by competition from the second. Actually, there are dozens of alternative explanations. I like particularly the one that hypothesized that maybe Neanderthals were victims of catastrophic epidemics, somewhat like it happen to the Mesoamerican natives when the Spanish arrived to the New World. Of course, there is not enough remains to prove that idea, but it wouldn't be unthinkable. At least I see it more convincing that supposedly different hunting techniques leading to a definitive advantage for Cro-Magnons over Neanderthals.
By the way, Neanderthals were Homo Sapiens too. Don't know why the author writes: "Neanderthals used thrusting spears to bring down tamer prey in Eurasia, while Homo sapiens, or modern humans, spent hundreds of thousands of years spear-hunting wary and dangerous game on the open grasslands of Africa.", as if they were different species. They were not. Taxonomy for Neanderthals is Homo sapiens neanderthalensis.