Maybe it's like languages where there are lots of local dialects--people in one village would be able to understand the people in nearby villages but not those a long distance away, even if there was no sharp break anywhere. I understand that was the case with the Germanic dialects (not sure if it is still the case today with more people speaking the standard national languages). People on either side of the Dutch/German border could understand each other even though standard Dutch is definitely a separate language from standard German. Supposedly you could go all the way from the North Sea coast of Holland to the German-speaking part of Switzerland and people in any area would be able to understand the nearby dialects, but when you are dealing with people a long distance away they can't understand each other. (Unless, of course, they both speak English.)
The analogy doesn’t work for me. Regardless of distance or distribution unless someone has changed the definition since I studied biology then by definition two animals who can produce FERTILE offspring MUST be of the same species. That would mean that “Neanderthals” who could interbreed with Cro-Magnon and produce FERTILE offspring were of a different species than the “Neanderthals” who could not do so. It would also mean that those “Cro-Magnon” and “Neanderthals” who WERE able to breed and produce FERTILE offspring were in fact of the same species regardless of what name they are called by. A St. Bernard dog and a Chihuahua are of such different sizes that they could probably never interbreed naturally but by artificial insemination a St. Bernard female could deliver puppies fathered by a Chihuahua male and they should be fertile and able to reproduce. This is because both are simply different breeds of dogs, NOT separate species in spite of the tremendous difference in size and appearance. On the other hand a Lion and a Tiger can produce offspring but the offspring will not produce a line of descendants because Lion and Tiger are two different species in spite of their similarity in size, build and predatory nature.