At this point, it just sounds like a matter of semantics. If "dominating your dog" means taking good care of it, setting it up to make good decisions, and controlling access to valuable reinforcement so that we can shape behavior, then there's zero difference between that phrase and the one I'd use: being a responsible dog owner. Which seems to me to make the use of the term "dominating your dog" completely useless. If "dominance" can literally mean "whatever the person using the term wants it to mean," then how can it be at all useful in a discussion of dog training and behavior? Especially if you have to add a caveat every time about how you don't mean "dominant" the way most people do.
Take the example above, that dogs pull on leashes because they think they are "leaders." In the entirety of natural history, only one species on earth has tried to pull another animal around by a string as a way of "showing dominance," and it sure wasn't dogs...that's a human trait. So in other words, you're projecting a human motivation onto a canine, and I'm at a loss to understand how that helps anything. I guess it's sort of an attempt to shame the dog owner, by saying they aren't "being a good leader," but why not just do the same thing by saying they aren't being an especially effective trainer? Or maybe skip shame-based approaches altogether.
There are many other explanations for why dogs pull on leashes that do draw from the study of canine behavior. For instance, dogs (and other canines) never walk at the pace required by most leash walks...walking at that pace is observably non-natural behavior. So it is reasonable to assume that many dogs wish to go faster during a walk, and may head out at speed until checked by a leash. Dogs tend to instinctively pull against pressure (opposition reflex, demonstrable via experiments). So it is reasonable to assume that a dog who hits the end of a leash will instinctively pull. We also know from experiments that most animals will continue to perform behaviors that are rewarding, so it's probably reasonable to assume that pulling on a leash is rewarding to many dogs (perhaps because the dog gains access to new things to sniff by pulling). So dogs pull because that's a natural canine behavior that's been reinforced via a learning process.
If I think my dog pulls because it is a natural instinct and a learned behavior, then my training plan is fairly straightforward: find a way to go from this (a measurable amount of time the dog currently spends pulling) to that (a measurable amount of time the dog will spend pulling, in this case, zero). I can track my progress! I can know when I achieve my goal! I can know when a protocol isn't having any results, and try something different!
But if I think dogs pull because they "think they are leaders," then my training job must be to "make my dog think something else." What our dogs are thinking is completely invisible and immeasurable. So my new job is to try to change a thing I cannot see or measure into something new that I cannot see or measure. Which is just pointless, as far as I'm concerned. This is how you end up with trainers suggesting that the crucial key to all dog training is to make sure you always eat before your dog, or always go through doors ahead of your dog, or never use food to train your dog, or all the other totally goofy, useless, made-up stuff that people come up with. None of which addresses the problematic behavior, except maybe by accident, some of which is actively harmful.
If we're talking about "dominance" as something that means whatever the person using it wants, or as a sort of invisible state of mind of our dogs, then all we're really talking about are the stories we tell about our dogs. Which typically tell us FAR more about the person doing the telling than about the dog. All that the persistent use of the term "dominant" tells me is that there are people who find the idea that their relationship with their dog is largely status-based very compelling. Okay, got it.
Personally, I don't think there's anything wrong with telling stories about our dogs, provided that the stories don't stop us from actually seeing the dog in front of us (which, all-too-often, they do). If a particular story I tell about my dog motivates me to treat her more kindly, play more fun games with her, or has other positive results, then good for me. But that's not how the story called "dominance" actually plays out for most dogs.
@the OP: I suggest actually reading some of the articles linked, since you claim an interest in the topic.