I wonder if the guy that posted that video checked with Hatsumi beforehand.
But Gekkan is a kata that I like. And I have been working on it often this year. And there is so many different ways of doing things from it. The end of one official kata variation almost links straight up with the next or another variation from another technique.
There is very little I think that can be conveyed by words and the internet to improve one's taijutsu I feel. And in this case, the one thing I think that can help others is to remember the lesson of Hicho no kamae no kata and set your foot down where you want it and where it can help rather than drop it anywhere it may land and try to work from there. I have seen people kick, drop their leg straight down and then try to take a step with it to power the take- down.
So if you have never been shown Gekkan, and want to prepare yourself for it, do Hicho while keeping that in mind. This advice might not help much, but it is the most help I think I can give considering the limitations we have.