Sure they did. We've even mapped their genome.
That link is just nutty theory. And proven in error as well.
Evidence that Neanderthals were fully human:
The FOXP2 gene supports Neandertals being fully human
http://creation.com/foxp2-gene-neandertals-human
Taking a crack at the Neandertal mitochondrial genome
http://creation.com/taking-a-crack-at-the-neandertal-mitochondrial-genome
National Geographic unveils Wilma the Neandertal lady
http://creation.com/national-geographic-unveils-wilma-the-neandertal-lady