NFTs are stored in a "wallet", the address is recorded on the blockchain. As long as you know your seed phrase (or other recovery key) it will be yours eternally. The NFT market is only a place to put buyers and sellers in the same spot. Even "in the market", the NFT lives at a blockchain address, someone else's wallet.

That's why Gamestop can say "we're shutting down our wallet service. Get your recovery key and restore your NFTs elsewhere"

Gamestop doesn't run a licensing server and probably won't. That's for publishers. Also, NFTs make licensing servers redundant.