Thanks. Yeah... iaido doesn't really get into kicking or punching. It's all about quickly drawing your sword and reacting to a surprise attack. It also generally assumes that your opponent is armed with a sword as well, so using your hands or feet to strike or block would often be a bad idea.
However, even though we don't get into those sorts of movements, the kata are still effective fighting techniques... if you do them at full combat speed and not the "demonstration" speed they're usually done at.
Also, the particular set in the video are done with very close combat in mind. The assumption is that your opponent is very close and that there's not much room around you to maneuver. In the other sets of kata, there's more moving around - there are a few kata in the other groups that even end up traversing almost the width of a gym. It's just this set is designed for use in a rather cramped space, which was part of its reason in the first place - you'd have had an advantage over any samurai who needed lots of space to fight effectively. It also means that I'm able to do this set in my basement... hence the video.
In a traditional school, iaido would have been taught as just one part of a comprehensive program that covered all sorts of combat situations, techniques and weapons, and those aspects of the school would cover combat scenarios that were different from what iaido assumes. Nowadays, it's considered a martial art of its own, so those other aspects of the traditional schools aren't studied by most iaidoka.
Cool. What martial arts do you study?