Your link does not work.
But there's a giant flaw in your calculations here if we assume your 100 billion figure is accurate. Which it seems that it is. So i was wrong about that.
Infant and child mortality was extreamly high in our primitive past. 50 billion girls born. Does not mean 50 billion girls grew up. If you want to estimate the number of girls (and boys) that even made it past age 5. You'll have to cut that number in half. And then there's another ~10 years they will have to survive to even have a chance of dying in childbirth. (Not the best phrasing but you know what i mean)
So, your 5-10 billion is starting to look a lot more like 2-4 billion (if we're being generous). Unfortunately for your argument. The boys that also grew up past puberty were all expected to be soldiers when called upon. You either fought and died or you just died. With some luck you survived. And by luck i mean lucky to have been born on the winning side.
The various empires in our history did not become empires because they were nice to eachother. They did so through blood and conquest.
Genghis Khan's conquests killed ~40 million people alone. That's estimated to have been 11% of the worlds entire population at that time.
Again. This isnt a competition. But men have always (unfortunately) been very resourceful when it comes to war and killing their percieved enemies. And there's been no lack of fighting, ever.
It's a bit of a trope but various massgraves confirms it. Kill the men. Enslave the women and children. (And then work them to death)