The study referred to has massive methodology issues when attempting to justify their position.
Firstly only 50 dogs/owners were included in the study and were only assessed once.
50 dogs is nowhere near enough dogs to test any association, if anything it proves how little the authors know about what is required to assess such traits and their development.
They also state
They seem to assume for some reason that who "wins" the game of tug of war somehow impacts upon the behaviour of the dog. Thankfully they found no relationship that who wins has little relevance to this debate."It is equally plausible that owners who are aware of the dog’s aggressive tendencies allow them to win possession of toys rather than winning causing the aggression. Longitudinal studies may prove useful in resolving this issue."
Enough about this flawed study, back to the subject.
Dog dominance is a massive problem, it usually starts with small things and grows. A dog in experienced hands can ofter play tug of war without any problems whatsoever. Sometimes not!
Same dog with an owner or family that know nothing about training may equal a disaster.
The behaviours start small and grow. I hear similar conversations all of the time.
It is so "cute" when he/she plays tug of war. It is so "cute" when they pick up a slipper/sock/cushion/towel and pull/run around with it. It is so cute when they get on the lounge/chair/bed.
I recall a very experienced handler with a GSD, his previous dog attained the title of U.D. so he knew what he was doing, when dealing with his quiet GSD.
His dog passed away and he got another dog. This GSD was very different and loved to play. this playing extended to the point where he would destroy leads and he had to wear leather gloves to stop the damage that the dog was doing to his hands, not to mention the leads.
I had an inlaw where the dog loved to play tug of war. He would happily start his own game with the household occupants. He grabbed whatever got the best reaction and ran, often chased by various humans. He got a wonderful reaction from them everytime. After which he generally got a walk, but if this was not possible he at least got some exercise by being chased. He got them up in the morning, he set when he was fed, he would simply start grabbing stuff until he was fed.
If this dog were assessed in the study cited his results would have been startlingly high as he absolutely loved to interact with his owners and everyone else.
Dogs are a lot better at studying and learning from us than we give them credit for. They generally know what is going on far earlier than we humans do. This is the reason why the "cute" behaviours may or may not become problems in the future.
I will happily agree that tug of war is not about dominance. It is simply a game that is played with a dog. It is what occurs afterwards that may lead to dominance, aggression or simply doggy problems. (Please insert whatever word, label or term you would like to apply as I hate arguing over the meaning of a words, like Dominant, Dominating and Dominance)