I think you mean it would not dethrone Dr. Gatling, whose contraption did indeed automatically remove spent shells, which illustrates just how fuzzy these questions of attribution are.
No, Gatling gun was a revolver-type gun, like a few before it, even though it's more automated. Modern Gatling guns, while immensely useful for rapid fire, are powered either electrically or pneumatically (I only handled two, both electrical). They also are damn heavy, because they have so many barrels.The early Gatling guns were gravity-fed, not belt-fed, and were significantly slower than the Maxim machine gun, and required the operator to rotate a crank to keep it operating, so it wasn't even fully automatic.
The Maxim machine gun was the first to offer really practical machine gun experience: a fully automatic weapon which is about as portable as a heavy small firearm, not like a light artillery piece.
Later versions did become more portable, but the Maxim was always a crew-served weapon. The advent of the fully automatic small firearm was really the Kalashnikov 60 atrocity-filled years later.
It's true that the Gatling required an operator to turn the crank and was significantly slower than the Maxim gun.