Ok looked at the vid and it seems that you have a problem with the gear inside the casing. If you take the side case off -remove kick start (1 bolt) then drain the oil, you should then be able to take the screws off of the casing, start with the ones by the oil filler, after you have that off you will see the kick start mechanism on the shaft, should be something like a spring and what I can only describe as a quarter of a gear, bit like the segment of an orange if that makes sense? then you can see what is going on inside, if the gear is damaged you will see that some of the teeth are damaged or missing or it might just be a broken spring, if its neither of those then it might be the actual kick start drive shaft that is worn or damaged, that will require much more than I can possibly do over the internet so you have to buy a manual for your bike showing the engine in exploded diagrams. It might be an easy fix but until you have it apart you will never know, the other option is to take it to your local Yam dealer and ask what it would cost to fix it. Hope some of that helped!! Good luck and let us know how your getting on.