Thats kinda a hard question to answer because categories differ depending on what convention you're submitting to. For the most part there are similarities for the broadest of categories like action, comedy, and drama but there can be very specific ones as well like this year at Kumouricon we have "Jidaigekki" and I've even heard of some conventions having an "Emo" category. Some convention don't even make categories until the judging just to make sure they can fill their time slot.
For the most part your video would fit in the Drama/Romance categories. (Usually those two are combined)