The list of arts is much longer than it really should be...
Muay Thai includes all the techniques of Kickboxing, plus some. I'd also argue that anything Taekwondo adds on top of that (unless you're doing forms or going for TKD-style sparring) is going to be flashy kicks.
"Grappling" is a generic term, not an art. BJJ and Aikido covers grappling, so that's redundant.
I don't know much about kenpo, but I assume it's also largely redundant with MT.
I agree that MT and Kickboxing is redundant, with MT having more techniques in it, however I disagree with the your point that the list of arts is longer than it should be. Just looking at the info provided on the school Konsei Martial Arts is a combined system that combines techniques from several systems of martial arts. They aren't claiming to teach all of the systems but rather a collection of techniques found within the systems, so since the body only moves in a certain way it is conceivable that while the techniques might look like they are found in several martial arts; the training drills, the training methodology, the application might come from one art that in a sense sets it apart from the other arts.
BJJ and Aikido are different so while they might take a technique or defense from Aikido, they might take another from BJJ that is not found in Aikido. Likewise they might take a move from high school wrestling (grappling), or to get out of a hold they might break the finger that isn't allowed in BJJ competition or in Aikido, but the principle (behind the finger lock/break) is learned from small circle jujitsu. While Modern Arnis (the system I study) has some sections of ground work in it, it is no where near as extensive as BJJ, JJ, Aikido etc. etc. and yet we have elements or influences from small circle jujitsu, some of my techniques I learned the principle behind them in an Aikijujitsu seminar and apply them in my Modern Arnis. It is an influence but it didn't come from Modern Arnis nor from the professor. So I will teach some "grappling" in my classes and state (to my students) that this technique has an influence from Aikijujitsu, giving credit where credit is due.
Kenpo is probably more of American/Chinese influence (I'm thinking along the lines of Paker Kenpo lineage) and therefore has more self defense related material than MT. So this too would be an influence that would be promoted to show where the technique, skill set, body of knowledge came from. It is completely different than the grappling arts, the MT/kickboxing, or the TKD.
The video looked like a cross between Muay Thai and Taekwondo, and not very fast. I didn't see much grappling at all. When the girl is doing speed roundhouse kicks, she's kicking maybe 1.5-1.75x per second. In our sparring club at my school, we're encouraged to do 2x per second for longer than that, and some are even faster. The important thing is this is the demonstration that they chose for an advertising video. It's not like it's a newbie who's just starting. Their techniques looked decent, but their speed was really unimpressive to me, especially for an advertisement.
I think the key is in your sparring club, your club has a different purpose than this club; this video is for demonstration, to entice the average viewer, the newbie thinking about getting into the martial arts, the average person who's has fear, who's kind of iffy about getting started etc. etc. What do they see? A girl of average looks that they can relate to, getting personal instruction from the instructor, struggling and being coached to overcome her fear, and then succeeding. I seriously doubt someone sitting around timing her kicks was ever thought about in the equation. I mean the average woman isn't going to say that "Her kicks are to slow, I'm going down the street to the gym where they kick two times per second, with the drill Sargent coach making them go faster and faster". No the average person is going to look at her and relate to her struggle, her looks, and say if she can do it so can I. And then possibly go down to the studio and take a class, then maybe sign up.
Now a hard core fighter or someone looking to get into the UFC type competitions might look at that and say "I want a harder core school" and that's fine with them (I imagine) because that is not what their school appears to be centered around. Look at any of their videos and you don't see the MMA fight club influence; the metal music, tattooed hardcore fighters, body piercings etc. etc. Instead it is around healthy living, and physical fitness, and self defense. As a promotional video I believe that is what is being promoted. I mention the girls looks because she isn't the supper cut, anorexic looking super model, she is someone that any person can relate to in her age group, healthy and fit. The people standing around watching the girl are the target audience (in a sense) Mom, Dad, and the kids. If these are the people you want to attract then you don't want to show "Lil" Johnny ground and pounding "Lil" Suzy. Even if she picks her self up off of the mat after taking the beating, hugging Johnny then raising his hand to congratulate him and turning around to the camera with a black mouth piece (so it looks like she has no teeth in her mouth). While the instructor and father in us might be going "You go girl", "Yeah that's my girl, she takes a beating and keeps on kicking", or "I pity the boy who messes with her when she 16"; the moms there would be saying "Not only No but HELL NO. Let me at the kid who was hitting my daughter, I'll beat the crap out of him!"
Another art that combines different ones together for the purposes of self defense is Kajukenbo, that might be a good one to try.
True Kajukenbo is a great art for the purposes of self defense, the problem is that it's not an art that is found everywhere.
