Open that video, cover the game side, and try to focus on the road/horizon point.
If it isn't bothersome/tiring to you after the 2mins, you have some good eyes.
It does, but inside the car, your body is moving too (not at the same degree of course) and your head/neck too have stabilization movements, so unlike Shift (as posted by SolidSnakex) likes to translate the vibrations and accelerations/deceleration and lateral forces, on your body, they hardly occur at a velocity or frequency to produce such pronounced visuals.
Granted, when you hit the already slowing car at your front and go from 120km/h to 40km/h in a split second, the game doesn't translate that at all!