Earlier quoted context omitted.
I didn't, never used it. So it's an app that hails you a taxi. Does that make Uber a taxi service?
No, unless they're paying the drivers. They're basically providing an interface to find taxis. Just like how Amazon can sell you a pack of Coke without being a food manufacturer. Or blogs can bring affiliate traffic to Amazon without being PCI compliant. Kayak and Hipmunk can get you a plane ticket without being an airline company. Etc.
There are plenty of definitions of the word taxi in many languages that simply mean a person transporting you from a to b exchange for money.
Doesnt say it gets exchange with the driver, nor are you saying that uberdriver drives around for fun and games. He does get paid to transport people from a to b. The typical business of a taxi service :)