You don't need an explicit contract, you can purchase something from someone locally with cash and own the item you purchased - it's a legal assignment of ownership in that there was a verbal agreement to purchase something at a specified price.
With NFTs, the purchase is even stronger than a verbal agreement since the 'legal contract' is the agreement to sell the NFT as a specified price in digital currency. Once again, ownership doesn't have to mean owning the intellectual property, with an NFT you 'own' the combination of bytes that you purchased, even if you don't have exclusive rights to those bytes and even if the original seller can keep making more of the exact same thing you purchased. It's like how you might 'own' a pair of sneakers - chances are those sneakers weren't produced for your exclusive use and tens of thousands of people also own a pair that looks just like yours, but you have every right to sell your pair and transfer ownership to someone else.
Again, the NFT itself is not adding anything. If you have possession of a physical object or an agreement from someone else transferring rights to you, you don't need an NFT. If you have an NFT, you still need the documentation showing that the person who sold you the NFT had the legal rights to transfer the referenced object as well as the NFT — otherwise you've paid for a receipt for “Bridge, Brooklyn x1”.
With NFTs, the purchase is even stronger than a verbal agreement since the 'legal contract' is the agreement to sell the NFT as a specified price in digital currency. Once again, ownership doesn't have to mean owning the intellectual property, with an NFT you 'own' the combination of bytes that you purchased, even if you don't have exclusive rights to those bytes and even if the original seller can keep making more of the exact same thing you purchased. It's like how you might 'own' a pair of sneakers - chances are those sneakers weren't produced for your exclusive use and tens of thousands of people also own a pair that looks just like yours, but you have every right to sell your pair and transfer ownership to someone else.