Well, if there was any actual science in that video, I missed it. That said, Airtabs are just vortex generators, which are very commonly used in aircraft design. I have tended to be a skeptic about stuff like this, but the principal is sound. NASA claims Airtabs as a "spinoff" of their research:
which is a little closer to "science", although not exactly from a disinterested source. My best guess is that they DO work, but the size of the effect, if actually measured in a rigorous study would probably disappoint. I have tried and failed to find such a study of real-world applications of Airtabs that was scientifically convincing. Not surprising. Who would fund such a study?