From your link:
"The great problem with all the Neanderthal art is that they are one-offs. What is different about the art of modern humans when it appears 35,000 years ago is that there is repetition - animal sculptures and paintings done over and over again in a recognisable style.
"With Neanderthals, there may have been the odd da Vinci-like genius, but their talents died with them."
Actually, they worked a lot of stone, they even made some very good stone tools. But to call a rock with a few lines scraped into it "art" illustrates what a gap exists between their species and ours, in that respect.
And yet their tools were often as well-done as those of contemporary anatomically modern humans.
It wasn't a lack of skill that was holding them back. It was something much more fundamental.
We have examples of gorilla and chimpanzee "art" too. It's about the level of the Neandertal "art" you showed me.