The article lists several art marketplaces. Do the respect the unique identity of a peice across them or could two competing marketplaces both sell “the one and only Mona Lisa”?
They respect the unique identity.
It's not clear how this could be enforced. Most sharply in the case of a hard-fork, and less sharply, but more commonly in the case of competing alt-coins striving to be the NFT of record.
I remember hearing that it's common practice to patent inventions in multiple different legal jurisdictions, to protect yourself in multiple localities. Otherwise, you would find your patents being exploited in a different country, where the registry of ownership that the government enforces is different.
In the world of NFTs, there is no enforcement of the registry. Competing registries are cheap to create. What's the value in that world?