Yes and No. Think of Art NFTs like artist signatures. in the real world, the scarcity and authenticity of artists signatures the books etc. make these valuable. have the same book with a different persons signature or no signature and the book is just as good as any other book with the same content.
With the Nyan Cat NFT, the original creator once approved it and said something like "This is signed by me and should represent the Nyan cat nft." However owns that NFT now this unique NFT on the ledger. The community aggrees, that the artists statement netters, so that decides which Nyan cat NFT is the correct one. If now I announce on twitter, that anither Nyan nft that I created is the "true nft", people wouldn't (or rather shouldn't) trust me, because the social consensus and history shows, that they've agreed upon a different Nyan NFT.
if I want that nft, I have to buy it from the current owner. If I buy it, I can tout about it on social media and prove my ownership on the block explorer.
Such things were only possible with non-digital artworks before. The problem is, that if you have any company, who manages this ledger, people would have to trust them - and there is also no company who has emerged in the part who would represent such a "social concensus on digital art signatures" - and with Blockchains it's too late to found this now.
This is just one of many use cases of NFTs.
In the real world, we have artists signatures and people buy them for high prices because they value that and are willing to pay for it. (Whether you like it or not.) The same holds for NFTs as artists signatures. However, with NFTs everyone can still "experience" the original because the data is still copyable as much as possible.
There are many other use cases for nfts. One is digital subscriptions which ought to be neutral and not owned by a single company. As an example, theoretically you could buy the licence to watch Inception (movie) as an NFT. Then you can go to Amazon prime / Netflix etc. and after checking that you own one such NFT, they'll let you watch it for a small streaming fee instead of requiring a hefty subscription fee per months after which you still don't own the rights to watch it forever. Requiring that such platforms support this could be enforced legally. Yes, piracy is an alternative today where you can still watch it forever - but it's strictly speaking not financially sustainable. However, I'm aware that the financial distributions when buying DVDs or cinema isn't exactly fairly distributed - but that's another bigger story.
NFTs are an abstract concept of rather neutral non-counterparty-risk of non-exchangeable limited ownership. In the non-blockchain world, it's the social consensus which says "Hey, the ownership ledger is managed by the government and we decide to trust that." - which makes the rest work. When people agree, that the non-government owned ownership on the Blockchain ledger "is the social consensus that matters", then people decide for it and the rest also works out.