Yes, when I take the time to slap one together. I focus more on how the game is played and the flow of the game itself. Like when I was supposedly making game for the LudamDare "Deception" challenge I did a quick 4 page Web of Deceit Design doc. I didn't focus on genre or audience. I wasn't looking to target set genre I let my game mechanic chose what it would be. As far as audience I ignore that too because sometimes what we think one audience would want actually attract another audience IMHO. I do what story I want to tell and those who find a interest in it will play it.
So in my Web of Deceit Design Doc. I state the premise and what needs to be achieved at the end. I then create what characters might be met in the process of the game, the locations, any needed dialogue and what needs to be done to achieve certain things. I use that as my starting base and as I develop that DD shifts and changes from there.