I know we are pretty far through the looking glass as far as the semantics here, but surely if someone is self-employed, they would be the business entity that created their job? "Job creation" is kinda a nonsense thing to brag about, so I have no idea what the standards are, but just linguistically speaking I'd assume self-employed=self-job-created.
Yes, it takes someone to sign the contract to do the work (for self-employed), or post the opening and hire someone (for an employee).
But it also takes investment. Many self-employed jobs sit on a platform that someone else is investing in. For example many construction workers are self-employed, but there needs to be a construction project for them to work on. Many folks in the film industry are self-employed, but there need to be movies for them to work on.
And in the case of Uber and Lyft, even if we call the drivers self-employed, they can't employ themselves in that particular way without the platforms that Uber and Lyft provide. The software is a big part of it, but so is the customer base (an asset in its own right), and the marketing that keeps and grows the customer base.
That's the extent to which Uber and Lyft can claim to create jobs. It's more like they create an environment or platform that enables other people to create their own jobs, but that is hard to fit into a soundbite.