I haven’t heard about those. Unfortunately, concealed pits don’t stay around for over 30,000 years and how would you see an over-the-cliff hunting strategy?
What are found with early Homo Sapiens are spear heads, fish hooks, etc. Fish hooks are found in South Africa and date as far back as 50,000 years ago. These aren’t associated with Neanderthals. All Neanderthals had were hand axes.
Running after game probably predates Homo Sapiens. Homo Erectus had long legs and could run. Their body style matched modern man. Neanderthals probably rand down their game too. It’s just that once they ran down their game, they jumped them with hand axes rather than spear them.
The world entered a long dry period about 75,000 years ago and Homo Sapiens apparently were forced to retreat down to the South coast of Africa. This is about the time the first fish hooks are discovered. It is possible that Homo Sapiens had fish nets too, but those don’t preserve very well. Modern man almost became extinct during this time, but apparently by increasing their diet to include fish and hunting more efficiently with spears, they were able to survive.
Once the dry spell was over, Homo Sapiens moved up Africa and where ever they settled, whatever Humanoid species was around disappeared. There were several archaic species of man, and Neanderthal was only one of them. Even Homo Erectus and several species of australopithecus were still around at that time.
Homo Sapiens were very efficient hunters and where ever we spread, large mammalian species quickly disappeared. Some archeologists say it was climate changes, but the coincident of extinction and modern man arrival to a particular area are strong.
It is possible that we simply were able to out hunt the other humanoid populations into extinction. Maybe we needed spears because we simply aren’t big and strong enough to bring down a rhino with our bare hands and Neanderthals were. But, once we got spears, we were able to be more efficient hunters. Then, maybe Jarred Diamond is right and it was probably a pathogen.