I don't see that as obvious. Why couldn't each company pay their robot employees a wage, and the robots buy the goods produced by the other companies and put them in a building for a few years before moving them to landfill.
The exact same pattern as our current economy, which apparently holds itself up, but without needing humans to be involved.
By why would the companies do that. The robots are a distraction, the companies in that case are buying and storing the goods from other companies. Why would they do that?
I have no idea how employees-buying-goods sustains our current economies (although I suspect it doesn't, and that they are inflationary, debt driven, and unsustainable).
Why would robots, or more accurately the companies that own them, buy goods from other companies outside of those needed for the company's own business? There's no incentive to do that.
As to why, the inevitable conclusion is: Company A and Company B make goods which do not sell: both go out of business. Company A and Company B make goods which sell: they stay in business. In a world with no human labour, organizations which want to propagate their own existence will do what it takes, including trade agreements with other organizations.
As long as the agreement to purchase each other's goods is backed by a chain of buyers ending in ever-growing and infinite fiat currency debt, it would be as stable as a real economy. And they could compete for each other's robot's coin to affect profits.
And the question of "is it providing utility for a human" is ... utterly irrelevant.