This seems like circular logic. First one has to define what a "Neanderthal" is before answering that question.
Yep. A lot of taxonomy is like that.
In the process of classifying things they're trying to find or define sharp boundaries on a subject matter that is actually a continuum.
I recall, in my first encounters with the subject, trying to get a coherent definition of the distinctions between species, genus, family etc.. The instructor was utterly uanble to provide one. (Of course this WAS at the junior-high level.)
DNA technology is also substantially revamping the whole field. Previously they had to infer what genes various organisms had by observing their expressions in morphology - which makes it hard to track genes that are there but "turned off". Now that they can actually sequence the DNA (or the expressed protiens when the sample is too old for DNA and RNA to survive) a lot of the classifications are getting rearranged.
Was Neanderthal a species, or something more akin to a colorform? What constitutes extinction when a branch that once interbred with another dies out, but leaves behind a substantial amount of its DNA? Did the two branches actually "speciate", i.e. separate to the point where the COULDN'T interbreed, or at least couldn't produce viable crossbreed offspring that could produce offspring of their own in turn? Or was it just that they mostly DIDN'T interbreed? Were they like the races of the current human species (clusters of different traits but one big gene pool), like horses and donkeys (where crossbreeds are easy but mostly infertile), or like fully-speciated organisms that might try but just can't produce offspring? Did they go extinct, or did most of their traits just gradually (or suddenly, as in a near-extinction event where all the copies of a gene were in the places where everybody died off) get lost from the geneome of the one big human family?
Seems to me it's mostly a matter of definition and partly a subject for more research.
Don't ask me for an authoritative definition. I'm just another observer, not a taxonimist. B-)