The idea behind NFTs as art is that they create a kind of scarcity for digital art that already exists and drives the value of physical art. The theory is that the reason high value art has such high value is because of its scarcity and not because of the inherent value of the art.
Let's think about this by way of analogy. Let's suppose an old painting was discovered. It had never been seen before, but some art historians examined the painting and concluded that it could possibly have been made by da Vinci, but more likely it was done by one of his students or someone else entirely. That painting might now have some value. It could potentially be sold at auction for a decent amount of money. Now let's say that forensic research is done on the painting and it's conclusively proven that the artwork was created by da Vinci. Suddenly that exact same artwork is worth a fortune.
In fact, you can ask your exact same question about paintings. Is any painting really worth millions of dollars on its own? Do paintings have any inherent value? Why is the identity of the painter relevant to the underlying value of the artwork? The quality is no better than it was before we knew it was a da Vinci. Its state of preservation is no different. All that's different is that we can now know conclusively that it was created by da Vinci. The "inherent value" of that piece of art is whatever it would sell for if it were made by any random anonymous painter. The fact that it's worth a fortune is because of its known provenance coming from da Vinci. NFTs work by establishing the provenance of a digital asset.
Imagine you wanted to buy the "official" Nyan Cat. The way it works is the well-known owner of the work issues an NFT representing Nyan Cat. That NFT is non-fungible (hence the name "non-fungible token") and is always owned by a single individual. It can be transferred or whatever, but it will always be unique. The history of transfers of that token is public and can be traced back to the original creator.
This is what makes NFTs scarce. Can any random individual make an NFT of Nyan Cat? Sure. But it wouldn't be worth anything because it wasn't created by Nyan Cat's known creator. That's like an art student copying da Vinci's work. Could the creator make multiple NFTs? Actually yes. This would reduce the scarcity of the NFT and possibly make it worth less. That would be analogous to a physical artist making multiple copies of their work. Although there would still always be a "first issue" NFT which may be worth more than others.
In the case of the article you mentioned, NFTs representing the artwork are being minted by the owners of the physical paintings. Perhaps that's what makes these NFTs valuable to some buyers despite the artwork being in the public domain and anybody theoretically being able to mint an NFT of it.
Note: This argument only truly applies for extremely notable works of art or artists. I 100% agree with the other answerers who are saying there is currently an NFT mania and tons of junk NFTs are selling for ridiculous amounts of money because of the hype. I'm just pointing out an actual real useful application of NFTs.
Furthermore, there are many other applications of NFT technology that aren't about selling works for enormous sums. For example, you could easily imagine an NFT-based DRM mechanism that only allows the holder of an NFT to access some medium. This could apply to run-of-the-mill music or movie sales at completely normal prices. NFT-based event tickets are already a thing that exists, making the transfer of tickets on secondary markets much more controllable, safer for consumers, and beneficial to event hosts. With some imagination, you can come up with many ways NFT technology can be used to solve real, practical problems.