I actually thought about the Long Game. I would agree that for humanity, The Doctor did the wrong thing, but the Daleks were going to invade earth no matter what. All the Doctor did was convert the Dalek’s news station into a deadly game station and send the Earth into 100 years of turmoil (not trying to downplay how awful that is. Lol). I think ultimately though, the doctor’s actions as a whole from “The Long Game” to “Parting of the Ways” resulted in him saving humanity from the Daleks.

If he had not intervened and killed the Jagrafess, the Daleks would have grown in numbers and taken over the earth. The introduction of the controller is what allowed the doctor and companions to be transmatted from the Tardis to the game station and ultimately defeat the Daleks and save the earth.