The "central authority" is the blockchain, which is decentralized because no one controls it.

> a limited edition skin in a game needs the central authority to make it usable in the game. So why do they need blockchain?

Why do you need a central authority to make it usable? I believe anyone can check the ownership of an NFT on the blockchain. You would just need to cross-check a player's game account against their blockchain address.

> a blockchain piece of data is accessible to all, so why pay for it?

It is accessible to everyone, but only owned by one person.