Quite simple: displaying an image may be the end result of both games and video, but the process of getting those images is totally different. Video games require the entire image (frame) to be generated from scratch using all sorts of player and game data. Your machine has to do all the work of figuring out how the light will hit every object, where the lights are, how bright they are, what the shapes and textures are of the various items, and so on, dozens of times per second in order to be considered playable. Video, on the other hand, is pre-rendered: that is, it had already been fully created before it came to your machine. All your computer has to do is load the images using the correct codex and display them.
Of course, it's actually quite complicated, but that's the general idea.