Can it be defined as property? I could make a Internet The Second using isolated networks and advertise whatever I wanted. It's not like digital movies and music where it's defined as property under copyright law because it's a creative work.
This is the same as saying no one can own a Disney character because anyone can draw it at home. Or no one owns songs because you can freely transmit them between devices you own.
People still own those things in most jurisdictions around the world.
The thing with Disney is that those characters were created by someone in a creative pursuit. IP addresses, on the other hand, are simply pointers to some location, and so it's an unknown if they can be covered under IP law. Digital copies of media only count as property because of that IP law, or they would be worthless because they can be copied infinitely.