Taxis also charge by the minute in many cities (in the U.S.) to account for traffic delays. In L.A., it's $0.30 for every 37 seconds spent waiting in traffic. (There is no charge for time spent on the move, as that is folded into the distance-based charge.)
EDIT: If the guy had taken a taxi instead of an Uber, they would not have been able to levy additional charges what he paid (which raised his bill from $200 to $600). That's the downside to Uber and Lyft: the price you see in the app is not the final price. In a taxi, it is.