the hotels role upsets me more than the taxi games, that is standard and there are signs and information on the rules if you look for them. The drivers comply quickly when called on the game ime, but the doorman is a "trusted" resource related to the hotel and they have responsibility for letting him line his pockets at your expense.
The doorman definitely got a kickback, the meter definitely needs to be running. It could be the taxi was heading in for the exchange (driver switch) about the time you were leaving and getting the fare, means the guy isn't driving to the drop with an empty car.
I would send an email to the hotel gm I expect you will get a response