[Alex Murphy]

Additional new research by Sorensen determined these sophisticated, rough-and-ready humans probably started to go extinct around 35,000 years ago due to diseases carried by modern humans, with whom they coexisted and may have mated with at the time.

And thus the argument that Neanderthals actually invented a primitive form of time travel was advanced....

[allmendream]

They mean biologically modern humans, not modern humans in a temporal 21st century sense.

Biologically modern humans have existed for around 100,000 years. If Neanderthals went extinct 35,000 or so years ago, that is a long time for both Neanderthals and (anatomically) modern humans to coexist.