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.
Dude, I hate to break it to you, but just because you choose not to, doesn't mean that a bunch of people do. There is literally a whole industry supporting it. You choose not to with your games, that is cool. I have played both ways, depending on the group, either way could be better. Some people need more visual que, some don't. Some people like to have custom 3D minis printed up that they paint that represents their character, and like to play with more interactive mediums rather than imagination (even though they also are using their imagination).
Some players are DMs don't like using starter kits, or essentials kits. Some do. My whole comment was simply saying, that yes, depending on who you are playing with. Boards, flatscreen play tables, coffee tables set up with blocks to be a dungeon all are used. Also with essential kits they provide them for premade adventures (though usually they are cheap paper maps that fold out on coffee table).
Though DragonSnooz is correct in the definition between a tabletop and a boardgame. The real difference is, D&D is a tabletop, but can use boards, but isn't a "boardgame". So my original sentence of "technically" is wrong. But it is still game that can used a board but overall it is tabletop, and is not a classic boardgame.
*edit: also a boardgame is usually a competition between 2 or more players, where D&D is the co op play of 2 or more players. But the definition of boardgame is "Board games are tabletop games that typically use pieces moved or placed on a pre-marked board and often include elements of table, card, role-playing, and miniatures games as well. Most feature a competition between two or more players".