However, for all the NFT features (mainly being able to reliably transfer ownership without relying on any specific company) you do need a blockchain.
But you're going to be relying on a specific company anyway to host your asset. The NFT itself is nothing but a certificate. People who buy fancy guns in Ubisoft's new game might represent them as NFTs but that means nothing unless Ubisoft puts them in the game, keeps them in the game, and keeps the game state updated with the blockchain state, which they can stop doing at any time.
In fact, this has literally happened before. Crypto stooge Calvin Becerra had a bunch of his NFTs stolen, and Bored Ape Yacht Club declared that they will start ignoring the blockchain and unilaterally declared that the images belong to Becerra, even though the blockchain says otherwise.
Technically you absolutely can run a centralized blockchain and mint NFTs on it (EVE Online did this recently in their latest Alliance Tournament, where IIRC the corpses of player characters who were killed during the event became immortalized as NFTs on an isolated branch of Tezos that was created for the event). But at that point congratulations, you've just made a worse database. The only point of blockchain tech is decentralization (if you care about features and not just branding your product with the latest hype).