He mentions tribes, and there is no evidence of tribes existing prior to 10,000 years ago. Which is about 25,000 to 30,000 years after the cave paintings in Chauvet and El Castillo.
Not that conflict never happens between hunter-gatherer bands, but evidence is it was, and is, fairly limited.
Real conflict and war started ramping up 10,000 years ago, with the dawn of slave societies and empires.
There's not a lot of evidence for war, but there's not a lot of evidence for anything. Very little survives over time. So I don't think a lack of evidence is meaningful yet.
Prior to 500 years ago there was little modern contact with the Americas, Australia, parts of sub-Saharan Africa etc., so observation of lack of conflict in hunter-gatherer bands there is more evidence. Obviously I mean hunter-gatherers, not the Aztec warriors.
I don't see what chimpanzees have to do with humans, unless chimpanzees are sculpting Venus Madonnas and drawing buffalo on caves.
I think this myth comes from early studies, who wanted to see this, and observed no warfare during the 6 months they spent around 20 people. Later studies asked these 20 to reconstruct their family trees & tabulate how each great-uncle died, etc.
(The other possibility is definitional. If we define war as involving thousands of soldiers, then obviously this never happened until societies which could co-ordinate thousands of people arose. May as well define it as involving uniforms & automatic rifles, too.)
We can also see glimpses of prehistoric societies from looking at people who stayed isolated from modern society. The Sentinelese people are a group example as they are one of the only remaining uncontacted peoples. [1] They are a violent warfaring people whom have murdered numerous people who have gotten too close to them. And there's nothing to blame here except their, and 'our', own nature. And one annoying aspect of society is that we must adapt to the lowest common denominator in matters such as this. Groups that are unskilled in warfare are rapidly 'replaced' (to use quite the euphemism) by those that are!
And as somebody else mentioned you can even see similar behavior in other non-human primates species from which we share a common ancestor, such as chimps. They, to this day, gather into bands in large part to go kill other bands and expand their territory. They also have a habit of engaging in some rather sadistic behavior to the losers. The only reason this warfare is not expanded to tremendous numbers is but for a lack of higher intelligence required to develop the tools and structure necessary for such. And as group sizes increase, so does the probability of splintering of a group.
So to appeal to the noble savage requires that we go war driven -> tranquil -> war driven. And that tranquil period is, conveniently, only when we have insufficient evidence to say anything one way or the other. This is not logical.
[1] - https://en.wikipedia.org/wiki/Sentinelese
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One final point should also be made since it's not commonly considered. Today live in what is almost certainly the safest period of human history - ever. Something few realize. Today there is less than 1 death per 100,000 caused by war - worldwide. The world population of 'humans' varies radically by era. But in the era's we're referencing, you'd be looking at a max population of some single digit millions. If they were comparably safe to today, you'd see some 10 or 20 people dying as a result of warfare per year - in total. I don't think it'd be be controversial to suggest that number was likely markedly higher.
There are no modern uncontacted hunter-gatherer bands to observe. The Sentinelese have everyone from local fishermen to American Christian fundamentalists invading their island. The bands in the Amazon are being murdered by miners. Modern people attacking and threatening the Sentilenese and getting a hostile response says little - if they were invading other islands, that would be a different story.