It seems like many of the operations take significant polynomial time to render, I wonder how in video games they are able to do it so fast. I guess the power of the GPU parallelization efforts are at play here. Lots of similar calculations happening at once.
In games geometry are mostly pre-processed. So no actual geometry processing is going on during gameplay
to @philippe-eecs, as @bobcao3 mentioned, I do believe most game geometries are pre-processed. But there are situations where the player moves towards an object, so this object first appears very far away (in low mesh resolution), and then becomes closer and high resolution. I might be very wrong here, but I imagine something like a mipmap is happening. So the game preprocesses and stores different levels of mesh resolutions, and use different levels according to the camera's distance to the object.