Even with a 60 Hz screen this will be advantageous. If the application is fast enough to render at 120 fps, rendering at 60 fps means that the UI thread will be idle at least half of the time, so the processor will draw less battery power.
I would think the added power draw from rendering at 120 Hz would come from all the applications needing double the number of graphics-calculations they need at 60 fps.
By making it twice as efficient. Partially by using fewer cycles to compute but probably largely avoiding tiny waits that waste power without computing.