The car in the video is running a 24 plate so it was first registered March or later this year. It is therefore a newer car, not one from the original i4 reviews.
A DCT gearbox will lag if a gear change is requested in the opposite direction to the one it's programming has preselected. I have only noticed anything similar to what is demonstrated in this video when I've actively gone out of my way to try to confuse the gearbox, and to me it feels like he's doing something similar here to make the car look as bad as possible (he's not exactly driving it normally in the demo).
The responsiveness does seem to get better as you go from tour to sport to track (I note that he doesn't say what mode the car is in during his demonstration) and overall I've got no complaints about the gearbox performance in mine when I've been driving it on the roads.