Wonderful idea for a topic!
I'd like to add
Hors-Jeu - By David Dufresne & Patrick Oberli
Mainly an interactive documentary, with less game components. Still, the overlay of gaming works enough so even people who don't understand soccer - like me - can be tricked into.
Plus, Florent Morin is currently working on a Game Doc called Enterre-moi mon amour telling the story of a syrian man who stays there, while his fiancee is leaving the country. And he's trying to help her along the way through What's App. It's based on an actual story told by the french newspaper Le Monde
It's pretty hard to pin a definition of the Game Doc really. And definitions vary depending on where you're from, the documentary world or the gaming world. I agree with all the caracteristics you mentionned actually, it's a sane base to understand this genra.
To me, the hardest point would not be to separate Game Doc from Webdoc, but Game Doc from Serious Game. They look the same, in form of a game with a serious background, and can easily be confused. What I would say separates them is that Serious Gaming teach you something, a notion or a tutorial for something concrete, while Game Doc is shedding the light on something, from the point of view of an author. Both real-based, but with different ending goals.
That being said, there is a cool french canadian article about mixing gameplay mechanics and story since the very beginning, to read there: