The theory behind the 'alpha male' (which has been debunked by lots of research in the past decades) is that they make the dogs submit to them by using fear. A leader does not need to resort to this. They make a dog do what they want by earning their respect. And this goes from merely being the one that provides them with food and shelter, to playing games with them to satisfy their prey instinct or training to stimulate their minds. And you can also demand respect by asking them to "say please" for all the things you offer them, which is what NILF is about.
I strongly believe that if you are a good leader to your dog, you do not have to be constantly worried that your dog might try to dominate you because you averted your eyes when he stared at you or because you let him sleep at the same height as you, etc. They are insignificant details as far as I'm concerned.
The whole alpha male theory was based on studies of wolves in captivity. Since then they have discovered that wolves in the wild act completely differently as a group and the pack dynamics revolve around cooperation and strong family bonds, not around dominance and submission. Lots of interesting articles and books have been written on this subject.