Thanks for link.
It is an interesting idea but the experimental design is too weak to conclude anthing. There are many uncontrolled variables. There is no way that the four tanks started out the same. Also, there are no replicates, so, we don't know if the differences we see are chance or because of experimental treatment. So, don't change anything your doing based on this video. It is poor science.
I read a study on protein skimming that actually measures the amount of stuff removed and describes what is removed. I was not impressed with the amount of nutrient removed by skimming. I read another study that demonstrated that the skimmer can increase oxygen levels in the aquarium.
So, skimming does provide some nutrient export and oxygenates water, but depending on your system, you might be able to skip the skimmer, but not as a result of the video.