This article briefly discusses two scenarios for why modern non-Africans are more closely related to Neanderthals than modern Africans. The scenario that seems to be most popular at present is that Homo Sapiens populations interbred with Neanderthals to some extent after leaving Africa. The more complex scenario is that there was an ancestral African population that subdivided before modern humans left Africa, and that one of these populations was more closely related to Neanderthals and was ancestral to non-Africans. This would seem to imply that interbreeding may not be as important for explaining the shared DNA between modern humans and Neanderthals as previously thought.
But I find it unlikely that ALL of the Neanderthal-related people left Africa and no groups stayed behind. I don't THINK there are any such examples in historic times (if someone knows of such evidence, I'd be interested). Sure, there was a potato famine, and many Irish people left, but Ireland was NOT depopulated! The Japanese left Korea a long time ago, and their language is now quite different, but they are genetically indistinguishable from Koreans, because the Koreans stayed behind.
So it seems to me that Occam's Razor (?) applies, and the simplest explanation is the best, unless evidence comes to show the contrary.
The Japanese must certainly have at least some admixture from the people who were there before them -- most likely the relatives of the Ainu, a group which is distinctly different from the Japanese, and only exists now on the island of Hokkaido. And they are mixing in, and will probably soon disappear as a pure-blooded group.
But you really CAN'T tell a random individual Japanese from a Korean -- people CLAIM to be able to do that, but there is really too much overlap. Yes, some Japanese, show Ainu-like characteristics, for example being hairier than mainland Asians, or having very pale skin and brownish hair, and I have seen one man with a dark forest green in his eyes, as well as my ex-father-in-law, who had a high bridged nose. But I don't know if those characteristics can occur in Koreans as well, because I never lived there, and never had the opportunity to observe a lot of people.
And, of course, phenotype does not equal genotype -- Koreans and Japanese remain the same.
Maybe its going past me but I don't see where the article provides any evidence that a population of modern humans with some Neanderthal characteristics first existed in Africa and then migrated out. My take is that the article suggests interbreeding between Neanderthal and modern humans after undiluted modern humans left Africa. Per the article:
The research, published in the journal PLOS Genetics, provides a historical context for the interbreeding. It suggests that it occurred when modern humans carrying Upper Paleolithic technologies encountered Neandertals as they expanded out of Africa....The team estimate that Neandertals and modern humans last exchanged genes between 37,000 and 86,000 years ago, well after modern humans appeared outside Africa but potentially before they started spreading across Eurasia. This suggests that Neandertals (or their close relatives) had children with the direct ancestors of present-day people outside Africa.