There are other explanations besides your genocide theory. Probably what happened is they were out bred and absorbed into the larger Homo sapien population.
Yes, the dilution through interbreeding theory has merit, but it implies that the H. sapiens population was much, much bigger than that of the Neanderthals. Also, if I understand the DNA evidence correctly, it demonstrates that there was some interbreeding, but not enough for the entire Neanderthal population to be absorbed. So, it has merit, but not 100% clear.
The theory I find most compelling is the caloric deficit theory. A larger brain, larger muscles, and a more active metabolism (to maintain body heat while living on a freakin’ glacier) all require much more calorie input. A human functions best at 2000 Calories a day, and can survive indefinitely on as little as 400 to 600 (you spend most of your time sleeping but it can be done). Neanderthals, on the other hand, probably needed between 8,000 to 12,000 Calories per day just to keep from wasting away. One theory of European megafauna extinction was that the Neanderthals literally ate them all. It’s possible that the Neanderthals died from food shortage in light of the decline of the mammoth population. It’s also worth considering that this made Neanderthals extremely vulnerable to siege tactics; a band of humans could kill a Neanderthal village merely by harassing their hunting parties and chasing game away from their hunting grounds, and this would only take a few weeks at most. In theory.