Okay. I am not familiar with this guy in particular, but he's not the first to be working with channeling drive through tug, and that IS something I am very familiar with. I won't say one way or the other whether his stuff in particular is good. "Natural Dog Training" is a marketing name, it seems, for using tug to motivate a prey driven dog. It is extremely popular in all facets of high performance sport (Agility, Flyball, Disc Dog, and even the bite sports like Schutzhund) I can recommend others who use drive to motivate obedience: Susan Garrett is probably the best for a newbie to the method, even if you have no interest in Agility. She is better known than this particular guy you link to, so if I was buying DVD's or books, I'd choose hers hands down. That being said, this doesn't mean THIS guy's stuff isn't good - just that tens of thousands of people worldwide have already been using Susan's stuff with great success, and haven't heard of this guy. His stuff may be great. I haven't watched the DVD's. But I am pretty good at determining what type of method a trainer is selling when I read their site. I've been in dog training for a long time.
As far as the THEORY of tug motivating obedience goes: Yes, he is not wrong. You MUST control a dog through drive. You cannot squash drive. If your dog wants to chase a squirrel, you have two choices: either you have conditioned him to want to play tug with you more than he wants to chase the squirrel, or you lose him to the squirrel. You CANNOT teach a high prey dog to not chase the squirrel (prey drive) for reward in a different drive (food). It does. Not. Work.
Either people have dogs whos food drive trumps ALL other drives (I am lucky, this is my dog) or people have a dog that "usually listens... Unless there is a squirrel. Or other dog. Or someone throwing a ball."
Now. Caveat. Not all dogs have enough drive to channel into obedience. Sport folks study breeds, breeders, and lines of dogs extensively to get a puppy with enough drive. Especially in a non-traditional breed like a Chi.
What does this mean for you? Well, there are people who are really good at building drive. Susan Garrett has some good info on building drive, and maybe this guy does too, but I can't say for sure. What I can say is if you are working with a low drive dog, you will get VERY frustrated with a training program that assumes all dogs want to play tug more than anything in the world, without addressing what to do if your dog does not.
The other thing to consider is, if your dog is like mine and food trumps ALL ELSE (and yes, she was doing "puppy obedience" in the park with dogs, people, squirrels, etc off leash at 3 months of age simply for her "boring" dinner) then you may want to go with the flow and use a method that focuses less on building prey drive. Clicker training. Susan Garrett also uses a lot of clicker, but there are other trainers too...
Building prey drive is a challenge even for those with vast experience doing so. Some dogs just don't have enough drive to truly use it as a reward. My dog, for example, has a retrieve and tug now shaped with clicker & food. It was the only way to get the behaviour for her, and it is the first behaviour we lose if there's any stress or distraction. I cannot (yet?) use tug as a reward for obedience. Tug for her is an exercise like sit or down. In fact, she does sit & down with more enthusiasm than tug at this point.
If you're lucky, your dog will have intrnse drive for SOMETHING. Use that thing. That is more important than picking a method and trying to fit the dog to the method, rather than the other way around.
How do you know if your dog has enough drive for this type of method to work? Does your dog go NUTS for a toy in at least 2 or 3 different familiar environments? Will the dog tug willingly for several seconds, several times and not lose enthusiasm? What about if there are distractions? Bonus points if the dog either brings you toys to tug with/throw repeatedly, or will tune out distractions in new enviroments when you bring out the toy.
Like I said, if your dog isn't fond of tug, you CAN sort of build it. It will never be like it is with a naturally drivey dog. But you can still build a fun game... You'll just be working really hard and get frustrated fighting a losing battle if you try to reward a low drive dog with games.
Hope this helped!