by the time you go that far back the evidence is so sketchy it's hard to say. In my view the "favorite game" is a key part for stone age level of tech. It was group vs group but it wasn't total war, where you kick men when they are down, execute the wounded, and burn the crops.
Certainly wars of extermination are a large part of our heritage. Carthage is gone. How many stone age tribes were likewise exterminated utterly? Likely many. But the tribal wars that we saw with late-stone age tech in the Americas were (generally) not wars of extermination. The aztecs are the largest organized warfare tribe I am familiar with and their wars were very ritualized. The smaller tribes were ritualized as well, not all ritualized to the 'counted coup' level but the fighting was young men vs young men, raiding for mates, keeping territories, proving bravery for social status not wars of extermination. Part of the culture clash with the European settlers were the different rulesets. The Europeans found men tortured to death and said "barbarians with no rules!" and the indians found camps burned and women killed and likewise said "barbarians with no rules!" and it escalated into war of extermination.
Pinker wrote a terribly researched but very highly regarded tome called "the better angels of our nature" he argues our manners our, culture, has saved us from our barbarity. He botches mathematics, fundamentally misrepresents certain sources, and is really off in his own world. He's the source for the "humans are better now" crowd. I think he's wrong if that's not clear.

We don't just land in wars of extermination. We wage them. Absolutely we have. And we will again. War unleashed has horror that is beyond what you can bear, wherever your line is. I read a collection of interviews of women soldiers on the eastern front of WWII and the story of a baby hurled down a well still haunting a witness decades later fills me with fear. It means burning houses down, torture, rape, starvation, sadism. The worst humans revel in it. And as one tribe feels backed against the wall it sheds some rules. Then the other does. And they both find themselves in horror. But if you're not mentally against the wall it's different. If you, even facing danger, are facing somebody who is more like you than different, there because you were ordered you there because a politician was a moron...well jumping to "gouge eyes out" is a big jump for your average civilized human.
Both sides have a point but the analogy that keeps coming to me now is that "wars escalate like fights" so what starts as a ritualized fight (hitting the face is ok, kneeing the crotch is not) can escalate to eye gouging and curb stomping. Some of us make that jump quickly, some of us refuse, some of us slowly get there. The vast majority of us have a point past which we embrace total war personally. Our structures to wage war professionally tend to limit the progression and end it quickly (like a bouncer or cop). But 2 tribes without their elders calming them down, settling on a weregeld, or a professional competent army which ends the fight early, the fight will spiral out to curbstomping murder even if started as an honest barfight.