I hate to break it to you, but I do not play D&D at all with a board. I used to, but I have found that it slows play down even more with a board. I now play completely with imagination. I tell players what they see, give them options, etc. No board.
So, definitely NOT a board game. It is an RPG. The point is to create a character and put yourself in the role. I would actually say that D&D is more like a choose your own adventure story than a boardgame.