Can't be arsed to watch the vid but I've done the calcs in the past. From an acceleration perspective rotating mass is disproportionately influential, as you have to accelerate it both linearly and angularly.. so a given mass saved from the rims will have a greater effect on acceleration than the same mass removed from the frame, for example.
As the chap at the beginning of the vid states, input energy isn't lost, it's stored - lighter wheels will accelerate faster for a given energy input, but also decelerate faster. This matters on a course with lots of speed changes (so something tight and twisty) and of course if you're actually concerned with speed. On something like a tourer where you're coasting a lot and anticipating stops in advance it's less of an issue.
Wheel mass also affects gyroscopic stability, with less rotating mass potentially making the bike feel more responsive but also less stable..