Well, they did exist for hundreds of thousands of years...until our ancestors came on the scene 35,000 years ago (in Europe, that is). It was after that they went bye bye. I think our ancestors ate ‘em up.
I don’t think we ate them up, I think the lack of game caused by our ancestors, who had better weapons, caused them to eat each other into extinction. You will notice the tools found at the site were neanderthal, not Cro Magnon. When Homo Sapiens Sapiens made food scarce in one area they moved on, causing Neanderthals to resort to the only food left to them. They couldn’t compete with Cro Magnon and resorted to eating their own or face starvation.