This one is hard to explain, but here we go, the Refresh Rate of your phone (60hz, and 120hz) are different that Frame Rates. Increasing the refresh rate to 120Hz will not increase your frame rate. So yes, 120Hz does work for games, but if the game is locked at 60FPS then it will not excede 60FPS but those frames are drawn on the phone at 120hz. It is a bit complicated, and I am not good at explaining it, but you are basicly comparing apples to submarines.
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