Of course Uber (and Lyft) are taxis. It's a service that you call to have a guy in a car come pick you up and take you directly to your destination. It's a different kind of taxi, certainly, but it's still a taxi.

It's very fashionable right now for startups to pretend that they're really a completely different industry than the one they're trying to disrupt, to distance themselves from the stodgy image, but marketing rhetoric doesn't make it so.