I do not place any credibility in this article, since two of the science/archaeology magazines I subscribe to have debunked this theory in recent issues. They said that the expert doing these studies concluded that there was little or no interbreeding (and sexual contact which did occur was probably thought of as equal to abusing your sheep or cow) and that Neandertal genes do NOT exist in our background. The same expert also concluded that the genetic markers for the development of language were MISSING from the Neandertal DNA which he has studied, and that is the best proof that we do not have their DNA carried forward in our ancestors. For all practical purposes, they were a separate although advanced species, and they died out rather than being absorbed.
The fact that somebody's uncle Herman looks like one of them is just a coincidence