What would the money be used for, though? It does not serve as viable nourishment or shelter.

Money is, after all, just a record of debt to facilitate trade so that transactions do not have to be completed immediately. Consider your job. You work so you can eat, but you might not be hungry at work. So, instead, you offer your employer a loan. The employer issues an IOU (money) to denote the promise to give you food later. Then, you take the IOU to the grocery store later and hand it back in to receive the food promised.

But in a world where a few people own all the core resources (land, minerals, etc.) and have all of their needs met by AI, they won't have any need for trade. They'll summon the AI to deliver anything they need.

It seems the only thing it might be able to serve is a record of who gets what after civil war captures the spoils from those rich few. But said civil war will require significant effort from all, perhaps even against their will; which is quite unlike a UBI system.