That is pretty impressive. But it was the "understand it" part that I'm surprised about.

I guess the real question was: Does the sequencing of Neandertal DNA allow us to prove that they had insufficient empathy?

A recent study showed that the modern human genome and the Neanderthal genome are something like 98% identical (I'm making that number up; it's in the paper I read; the exact figure is fairly close to that). The 2% of genes that differ include the genes in modern humans linked to empathy, facial recognition, social aptitude, etc. (We found out which traits these genes are linked to because they are present, but not expressed, in modern-day people with severe forms of autism).

If I can ferret out the paper, I'll post a link.

Even better: https://www.youtube.com/watch?v=-1Nrm-M-m14