You really do need to read back through that part of the discussion ~ seriously.
Modern humans differ very little from one another when it comes to genes. Our biggest differences seem to be a consequence of epigenetics ~
Humans do differ very little from one another genetically, and looking at the observed phenotype differences makes it obvious that even small genetic differences can have a large effect, but that is not the point that I am making. There is still no proof that the observed genetic markers in some modern Humans (two according to the research) that happen to be the same as the observed genetic markers in some (three in fact) Homo Sapiens Neanderthalis are there because of reproductive interaction between the two species. They might as well say that Neanderthals have (say) the allele for blue eyes, and therefore every modern Human with blue eyes has some Neanderthal DNA.
It may very well turn out that there has been genetic input into modern Humans from the Neanderthals, but this research doesnt prove it.