This is incorrect. The ownership of private property occurred in the Feudal period. Capitalism is the creation of ‘surplus-value’, i.e. capital. This is different than ‘market-value’ which is the selling price for things.

Since WWI it is the role of the nation-state to create a market where capitalism can occur. This is to create the ‘rule of law’, but more importantly the economic system on which capitalism can occur. This includes property rights, but also human rights. The nation-state also defines citizenship, and has war making power.

This creates ‘first word’ capitalist countries, and ‘third-world’ pre-capitalist ones. War occurs as the capitalist countries exploit the pre-capitalist countries for cheap labor or resources. ‘Free Market Capitalism’ if it means anything at all, is the ability for capitalist nation-states to exploit pre-capitalist countries. We are seeing this occur around the world today.