The effect you're looking for is motion blur. You can actually get a "video game like" effect with a real camera too if a scene is very well lit and you chose a

The effect you're looking for is motion blur. You can actually get a "video game like" effect with a real camera too if a scene is very well lit and you chose a large aperture size and very fast shutter speed. It looks similarly jerky. What you suggest trying is actually possible with quite some games/engines. Some other commenter mentioned the source engine, I did it once with trackmania a good decade ago. It does very much amplify the feeling of speed.