If humans who don't own robots are not producing and therefore not earning, then they're also not buying. Who are the robot owners selling their products to?
See: "build me a bigger yacht", building moon bases, researching immortality medicine, and building higher walls and better killbots to manage any peasant attacks
Why would other robot owners need to buy anything? They can just get their AIs to figure out how to make the things they're buying so they can not buy them anymore.
I think it's likely that there'll still be specialization - some robots/AI will be better at some tasks than others. On top of that, physical/natural resources may be owned by different people. So maybe you need tungsten and I need someone to build a space elevator, so we trade.
