I equate "running" something to refer to a piece of equipment that is motorized. You are running that equipment only when the motor is running.
In my mind one can run a drill press, or a chain saw, or a generator. Until I see a motorized gun I will not use that term in regards to a firearm. It sounds ignorant to me.
The General Electric Mini-gun does have an electric motor, which enables it to have a rate of fire of 2,000 to 6,000 rounds a minute. So yes, one can "run" a mini-gun.
https://en.wikipedia.org/wiki/Minigun