What does the level of technological development or cultural sophistication have to do with determining species? We have people on this planet living in the stone age while others can split an atom. Yet, they can interbreed producing viable offspring which means they are from the same species.
The Neanderthal phenotype coupled with the complete absence of technological advance over hundreds of thousands of years indicates that they are a distinct species. There were and are some human groups that use very primitive tools, but there were no Neanderthal groups that used advanced tools.
It is problematic at best, which is why it is hardly definitive on its own, which is why Neanderthals are not conclusively regarded as a fully distinct species, because they clearly had inferior tools and inferior culture.
It is one of multiple factors that appear to point toward the same general direction, or at least don't contradict it. If instead Neanderthals and Cro-Magnons had very similar or indistinguishable technology and artistry, then that would be a strong signifier of intermixing, and a powerful argument in favor of sub-species, if not closer than that even.
But it is worth noting that in paleo-anthropology tool-making and cultural behaviors are conventionally regarded as the barometers of intelligence. Therefore, if the Neanderthals were clearly inferior to the Cro-Magnon in those regards, then it is extrapolated that were clearly less intelligent.
And finally, it is worth noting that it is a fallacy to craft an analogy between modern post-Industrial society and the pre-urban subsistence world of the Cro-Magnon. Back then, and until relatively very recent times (about 5000 years ago) the degree of technological aptitude or cultural sophistication was all but indistinguishable between humans worldwide.