True, I agree that contract law's existence in the first place depends on government enforcement. The same could be said for property ownership, at least state-enforced legal forms of property rather than direct possession (e.g. absentee land ownership proved via deeds and land registries, and enforced via trespassing law).

Within the context of the U.S.'s current economic/legal system, I think it's more in accordance with common usage to think of the existence of private property and contract law as being the basic substrate on which everything else happens, including more specific government action. For example, to continue with the property analogy, we typically think of eminent domain as a state "taking" property, even in cases where a person's "ownership" of a property depends on the government in the first place (someone owns a deed to land they don't actively reside on or use, but since it's legally recognized as property, the government choosing to build something on it is legally recognized as a taking of property). But point taken that this whole contract/property system is itself created and enforced by the state, not some kind of naturally occurring phenomenon.