You "own" it in the sense there's an immutable paper trail that proves you and you alone are the owner. However, the castle being protected as a national monument, you cannot bulldoze it or even change it in any way by law AND you are obliged by law to open it to the public.
Basically you are buying bragging rights.
This all feels very strange to me, probably because it is so intangible AND Twitter is still broadcasting the message just the same AND Twitter already has a concept of ownership which isn’t being honored here.
If I grab something out of your hands and you say, "that's mine!" That would be property.
But if I put up a painting and you ask, "who made that?" That would be credit.
There is no scarcity of blockchain space - you can download Bitcoin right now and use less space than the newest "Call of Duty" collection. The property is very easy to acquire.
But then if you ask "who made Call of Duty", you are forced to point to the system of IP law, which may or may not credit the individual creators properly.
So, what NFTs are trading is a particular form of credit. This tears up some economic assumptions around what credit is "worth". A popular blockchain is one that allocates credit accurately and fairly.
In a basic sense, you own a signed ‘snapshot’ of the tweet.
Basically it is kind of ‘only signed copy of the tweet’