Unlike AirBnB which breaks NY City and NY State regulations, Uber does follow NYC Taxi & Limousine Commission rules imposed on them and Lyft and other services. But in NYC, the Mayor's unsuccessful efforts withstanding, we aren't trying to restrict market entry and basically asking that Uber drivers undergo the same screening as Yellow Taxi drivers.
Read this part of the article:
"Uber made a particular effort to deploy the tool in cities where it faced opposition from local regulators or rival taxi and transportation companies. One of those cities was Portland."
NYC did not bow to pressure from rival taxi companies and they did follow the law cooperating with NYC Taxi & Limousine Commission (again, unlike AirBnB which directly broke NY City and NY State laws and was sued by the NY State Attorney General). Uber was never in trouble with the law in NYC nor NYS and the only time it has trouble are with entities that try to block competition from the regulated monopoly.