Alright.
1. This mixing of genes between Neanderthals and the other (sub)species happened at least tens of thousands of years ago. That's not too long in evolutionary terms, but it's long enough to make a significant difference.
2. Genes do not always determine our behavior. Mostly they just make us biased toward certain patterns of thought and action.
3. Even if genes did determine our behavior, it wouldn't have been a bad thing for our genes to have mixed with those of Neanderthals. Contrary to how their name is used in popular slang, Neanderthals were quite intelligent.
In other words, if you think that article indicates that our gene pool was polluted by genes that favor primitive behavior, you should re-read the article and study up on the science on which it is based.