I don’t think this is the place where an in-depth discussion of the worth of artistic symbolism and abstract representation is suitable. However, if you also accept, additionally, the hit-and-miss nature of the survival of artefacts, I think it somewhat precipitate to condemn Neanderthals as artistic non-compos.
Let me say I lean towards the theories that have Neanderthal & Cro-Magnon as being quite alike. The extinction of the former is not out of the ordinary: isolated groups of Homo Sapiens became extinct at different places & times, too. Small numbers of Neanderthal, pushed beyond the point of no return with possibly the most extreme Ice Age of them all, disappearing from the planet don’t necessary mean they possessed some innate flaw. After all, it was only a few years ago that most anthropologists denied the possibility that Neanderthal & Homo could interbreed.
However, as I alluded in my first paragraph, what you do with your “gaming” Neanderthals is, of course, up to you. I would hardly like to proclaim my historical gaming is beyond factual reproach. I just wouldn’t personally get too attached to an ingenious but still theoretical premise such as the Neanderthals couldn’t draw &, ipso facto, were severely handicapped as hunters.