What would they have competed for? There were few humans altogether in Europe, maybe on the order of thousands to tens of thousands across Europe (I assume, this is not known). They wouldn't need to ever meet.
We don’t really know very well how many humans (including Neanderthals) lived in Europe. We have pretty good estimates of effective population sizes from genetic data, but these don’t tell us much about actual population sizes beyond giving us lower bounds.
What we do know, though, is that hunter-gatherer peoples have very low population densities, and that these low population densities are a result of resource scarcity, and violent inter-group competition for these scarce resources. Other hunter-gatherer groups impact you even if they are miles from you.
Oh, and we do know that anatomically modern humans met Neanderthals, at the very least because they interbred.
This is meant in the context of genetic survival. Homo sapiens were, eventually, better equipped to reproduce and survive. And if you read the article, it mentions at the bottom that part of the Neanderthal genes have been... essentially assimilated into the Homo Sapiens gene pool. Hence why Neanderthals seized to exist, and other species that live in a vaccuum (island) did survive. Many Homo Sapiens today are also part Neanderthal.
What we do know, though, is that hunter-gatherer peoples have very low population densities, and that these low population densities are a result of resource scarcity, and violent inter-group competition for these scarce resources. Other hunter-gatherer groups impact you even if they are miles from you.
Oh, and we do know that anatomically modern humans met Neanderthals, at the very least because they interbred.