The concept of natural law would say that property rights exist. Rights, as a concept, are a human concept but it doesn't make them not natural. Natural rights are more of a recognition than an invention. Even in nature, many animals are territorial and stake a claim to a certain area. If there is anything "unnatural" about it, it is the fact that humans typically handle the concept LESS violently than animals would. Social relations are natural among both animals and humans.

Naturally, land typically cannot be used by "all" at the same time. If I'm running a business and using a piece of land in the process (or using it for a home), someone else cannot practically come along and use the same piece of land for their business at the same time without displacing the first person. Exclusive land rights can only be natural, it's just a matter of how you enforce it. Every man for himself (which perhaps would be more "natural") or a system of laws to protect those rights.