A bone? Sure. Land? Stock in a corporation? These are the property rights capitalism is made of. Entire cultures have existed well into written history without either concept (one of the things that made it easier to forcibly remove them from the land they lived on, which likely means that your "natural law" arguments for land ownership are insufficient to protect the property rights of almost anyone in North America).
What you need for capitalism is centrally enforced rights to things like land and corporate equity. That is not a simple extrapolation for protecting one's personal possessions any more than copyright is. And like copyright, they require a government.
As does the idea that governments are a magical prerequisite for property rights.
... just as humans invented land ownership around the time that became useful.
Try taking a bone away from a dog, and my point might seem clearer.