To run a video it is a simple playback of what has been recorded previously. Playing a game the computer has to dedicate multiple operations to running individual things. So if 1 thing plays the video is the same thing that displays what is on screen it would be 1 to 1. But then you move your character. That is a 2nd operation. Then you move your camera, a 3rd operation and so on.
Basically you are comparing running a single movie to running 100s of movies at once.
If you are ten: Running a game requires you to have enough processor speed to keep up with the information that is constantly being entered. Your GPU needs to then actively render all the images associated with what you are currently doing. Every input into a game changes what needs to be rendered and the GPU and Processor need to keep up with those inputs. Where as watching a video of a game is playing back a recording, may take some initial processor usage but will quickly turn into being simple playback.
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