The criteria is "a small company with at least 10 employees." Uber drivers would not count, neither would other independent contractors who run their own design or development businesses.
"examines trends in entrepreneurship—defined here as self-employment with at least 10 employees"
"Start-up" is such an abused term. I used to think of it as an endeavor searching for a way to monetize and fund a new idea, but it seems that it is used now to refer to any new entrepreneurial (thank you spell check) endeavor.
It isn't really "entrepreneurship" but I could easily imagine those people show up as small business owners in the official stats.