Of course they are, everything else is just PR at the moment. That said, they are (the first?) global taxi company. No one is surprised that global retailers, like e.g. H&M, have huge headquarters.
They're a company you can contact to dispatch a car to take you where you want to go that charges you by distance traveled. If that's not a taxi, I don't know what is.
They've already won vs taxis. Now they're going for courier services, buses, food delivery and even cleaning services. They aren't part of the sharing economy, they're trying to be the sharing economy.
Until they get their self driving cars, and then the are a transportation and logistics company.
But they definitely aren't a taxi company