How does it work "directly"?

I'm just curious about the technical logistics. I read elsewhere that at the recipient needs to connect to the internet before they can actually spend it, which would make sense if true.

Now the real magic would be finding some zero knowledge proof that destroys your ability to spend a token once you've already spent it. Like a one use signature for an NFT transaction. Each time you receive it, you have a verifiable hard cap on the number of transactions you can do with it. Then you wouldn't need a blockchain for double spend prevention.