My dog plays competitively with humans, or tries to. I don't play that game. It's a great way to get bitten, even though it's by accident.
I think play is a great way to bond with my dog. We both enjoy it. That doesn't mean I"m a play machine and play every single time he wants to. He is very bossy and demanding, and the more I give in to that, the worse he gets.
That doesn't necessarily mean the Alpha/dominant theorists are correct. It's just the way he is.