The imaginary property industry would look pretty much like it does now, but the content cartels would be hiring goons with bats instead of goons with law degrees.

There are a couple possibilities. One is a legal regime that separates copy-rights from use-rights. One would be a system for letting people selectively share trade secrets without risking someone else making the same product.

Essentially, they would enforce voluntary constriants on future actions, when those actions are made possibly by access to information known by another party. This amounts to a property right, though like our current property rights regime, it is relying on a legal fiction as a useful abstraction.