Mine definitely does this. I don't know if it's just my head, but I think I've found that it seems to behave differently depending on the state of the transmission. In neutral (manual), it behaves like the video... approximately the same in severity.
When in gear (driving, pulling away, etc.), it's much less severe, but you can tell that it's doing that if you had just previously driven another car. Otherwise you just get used to it. Personally I don't have really have a problem with it and I think it sort of helps me drive smoother anyway. My brother recently got a Mazda mazdaspeed 3 and it's at least 5 times harder to drive that thing smoothly as compared to the GTI.