I've been reading John Bradshaw's book "Dog Sense" and he has a lot of good points.
First, he feels the "alpha dog" concept is based on poor science: the wolf packs studied were captive wolves with little or no familial relations to one another. Real wolf packs are families and the rough stuff seen in those captive packs doesn't occur. After all, "alpha dog and bitch" are really mom and dad. The rest of the pack are their children from this year's litter and last year's and maybe the year's before.
Next (and I am giving you my take on this), if you were to take a wolf pup and a dog pup and raise them together in your house, you would always know which was the wolf. You could socialize the dog to like other humans, the wolf would only tolerate them. Also, the dog would naturally take to other dogs, whereas the wolf would only accept his pack. [What Bradshaw says is that when the dog and wolf parted company thousands of years ago, it was the wolves that could tolerate mankind that became dogs. Those that couldn't remained wolves. Following this, I guess he would say that if we killed off all the dogs, that would be the end of it -- we couldn't domesticate the current wolves.]
Bradshaw admits he doesn't have all the answers, but he feels, if we want to understand dogs, we should study dogs, not wolves. And we should study dogs in their natural habitat -- in human families. Reading his book may put you in awe of that animal at your feet!
Meanwhile, he sees the relation between dogs and humans in a family as between dogs and their providers/nurturers/mothers, not dog and alpha dog. He feels training should always be positive, not punitive.
I suspect that the "alpha dog" training proposed by the Kingdom of Pets works mostly because it causes the human to be consistent in their dealing with their dogs. Dogs are happiest when they know what to expect. Humans are happiest when they know what to do.