I don't think you'll get anywhere with the neo thing, but you are correct that there has to be a clear difference in order for neo to apply. Like with neo-shamanism. Shamanism ended. Then much later neo-shamanism started. It is not part of the same thing, it is something new using the original for inspiration. Same thing with neo-nazis. They are not a continuation of the National Socialist Party.
Thus making the neo- necessary. Plus with a clear break it means that there has been the possibility of neo-nazis to pursue ideals that the original nazis didn't. They are inspired by them, but they can and do have some ideological differences. For example a greater tendency towards anarchism in some neo-nazi groups. That makes them quite different.