Either we outcompeted them or they were more docile and we took advantage of that, or they kept retreating till they could retreat no more (if they feared interaction).

That's assuming homo sapiens were actually their undoing. They may have just died out on their own.

Or they haven't at all. Consider that people of European and Asian ancestry typically share some Neanderthal DNA, and the DNA difference between humans and chimpanzees is ~1%. Maybe they're just us.