They are not really exctinct, they are part of our ancestry, at least in most of Europe and those who migrated from Europe. One possibility is that when Sapiens met Neanderthal they simply outnumbered them because they came from more fertile/hospitable lands. Like Google acquiring an older but smaller company.
I don't think it's useful to consider a rare (0.2%) neurological disorder in this discussion, unless you're suggesting that Neanderthals had voids in their brain matter. This would be an extraordinary claim, being unlike any other primate or mammal.