Right, I don't get what atoms have to do with it at all. Today, I can buy an iPhone for $1000 that's a phone, camera, encyclopedia, game console and more and more. Just 30 years ago this would have required a lot more atoms (including energy input, I suspect) and a lot more money.
I’m guessing here but it seems to me the idea is that each atom can hold a finite amount of information and information storage requires energy. An economy requires information and storage of information (not necessarily permanently for each transaction). So it seems to me that the ‘economy’ is limited in size by being proportional to the number of atoms we’ll be able to have access to.
Consider Jevon's Paradox. Yes, we're more efficient at turning materials into products, but that just means we do it more, and the net consumption goes up. Did you replace your camera, encyclopedia, game console etc every few years, 30 years ago? Do you think we're mining less?