By calling them "H. sapiens neanderthalensis", the authors are tipping their hand. They view Neanderthal's as a subspecies. There are those who disagree. The definition of what a species is seems to depend on who you talk to.
There are examples of animals, currently classified as different species, being able to interbreed and produce fertile offspring.
e.g. Polar bears (Ursus Maritimus) and Grizzlies (Ursus arctos horribilis) can breed to produce fertile Grolar bears[1].
TL;DR: Although Polar bears and Grizzlies appear to be very different, they diverged relatively recently and have remained distinct mainly through geographic separation. They don't interbreed much because they generally aren't in the same places during mating season. Although their physical traits have changed considerably, genetic differences haven't yet built up to the point where their offspring are infertile.
It's conceivable that the different subspecies of humans were isolated from each other in very different environments and evolved along very different lines. However, they weren't isolated from each other so long that genetic changes made it impossible for them to produce fertile offspring.
There are examples of animals, currently classified as different species, being able to interbreed and produce fertile offspring.
e.g. Polar bears (Ursus Maritimus) and Grizzlies (Ursus arctos horribilis) can breed to produce fertile Grolar bears[1].
TL;DR: Although Polar bears and Grizzlies appear to be very different, they diverged relatively recently and have remained distinct mainly through geographic separation. They don't interbreed much because they generally aren't in the same places during mating season. Although their physical traits have changed considerably, genetic differences haven't yet built up to the point where their offspring are infertile.
It's conceivable that the different subspecies of humans were isolated from each other in very different environments and evolved along very different lines. However, they weren't isolated from each other so long that genetic changes made it impossible for them to produce fertile offspring.
[1]https://slate.com/news-and-politics/2010/05/when-polar-bears...