I'll elaborate on my thoughts a little, and try not to be too boring.
I agree that people are territorial. (Mostly, anyway. There's a rich history of nomadic cultures, too. Which might make this a good time to say that while I think it can be useful to try to understand human nature in order to generalize, one has to be careful. Whatever human nature is, it produces a broad range of distinct and sometimes contradictory behaviors both across and within groups and individuals.) I also think it's probably fair to say that there's some kind of innate idea about possession. It's also clear that humans often contest (with violence and/or negotiation) and regulate (with law and/or custom) access to resources. But how that's done and what the ideas about property are - what can and can't be owned individually and collectively, and what sort of privileges and responsibilities are implied by ownership - has varied quite a bit from time to place. According to JK Galbraith's History of Economics, the capitalist idea of private property has only one close antecedent in Western history (during the Roman Empire).
There does seem to me to be a consistent pattern of people forming groups (clans, tribes, nations) that could be more or less described as some kind of kleptocracy. As societies get bigger and more complex, greater disparities of wealth and power are possible - but not a given. Whether there's more or less egalitarianism has to do with other specifics. If your main point is that this larger pattern (kleptocracy) is something we've seen before repeatedly and can continue to expect, then I agree. If you look at history and see parallels to capitalism, I'm not surprised. There's an element of truth to the saying that there's nothing new under the sun. I came across an idea once (in David Graeber's book "Debt," I think) that all economic activity is governed by three principles - communism, hierarchy, and exchange - and that while one or more of them may be dominant in any given transaction, they tend to co-exist in most societies to varying degrees.
But while we've had numerous iterations of kleptocracy, it hasn't always been capitalism, and capitalism doesn't represent a natural state. For most of human history, markets played a small role (if any) in most lives. There's scholarship (the books "The Great Transformation," by Polanyi, "The Many Headed Hydra," by Linebaugh and Rediker, and "Empire of Cotton," by Beckert come to mind) about the transition to capitalism that make it clear that it didn't just happen, it had to be imposed on resisting populations. A left-leaning person needs to deal with the apparent tendency towards extractive hierarchies and consolidation of power, but it's just as important to understand that our current conventions aren't universal or eternal and that capitalism doesn't represent a way of living uniquely consonant with human nature.