Videogames also do the input every loop so there's a big difference there. It must be evaluated with a video only.

We're talking about monitors here, which usually have a mouse cursor on it for input. Of course it would be hard to tell between 60 vs 120Hz screens if you used both to play a 30FPS video.

Lots of games don't do input on every loop. Starcraft 2 has 24 hz input.