I think that it is unfortunate that today's layman associates role playing with D&D, and D&D sticks to the same archaic model of the game as in the early 1970's - i.e. a tactical wargame tied to toy soldiers (miniatures, or affectionately, Minis for hobby boys, just as the dolls for boys are called action figures, for marketing sake).
Still, there is no denying, that what makes D&D is it's game model. You can look at any game and say that it either feels like D&D, or it doesn't. Clearly, D&D framework is not appropriate to run every game, and at the same time, Indie games have developed new game mechanics, which never found their way into Dungeons and Dragons.
The big question is, what defines D&D as opposed to the other role playing games. One part that makes AD&D 1st Edition unique is its Gygaxian Naturalism. First coined by James Maliszewski, it describes Gygax's tendency to define everything in the fantasy world in game terms - i.e. give cats and mice, which will never be combatants in the game in any meaningful way, hit points.
I get this, there is a great big revolving fantasy universe, in which the adventure takes place, namely a dungeon labyrinth to be explored. Large portions of Gygax's DMG are dedicated to navigating that world on foot, in the air, by the sea and under water. There is a separate issue of the role of the story in AD&D, and the game's inability to model adventuring beyond the Dungeon Crawl, or as they are called now, site based adventures, but the bottom line, Crawl is the nature of D&D. This might sound tedious, if you stick to Dungeon and Hex Crawls, but it gets better if you adapt story telling modes to travel the fantasy world.
What makes D&D play D&D is this. I design and run complex adventures. What this means is that Dungeons are tied to (and controlled by) those who run the fantasy world of Midlands. Before they start adventuring, player characters do not run into the fantasy game equivalent of the general store, buy weapons and armor, then to Tavern for clues, and finally to the Mother Lode of a Dungeon as if they were the California 49'ers and the Dungeon is their staked claim. Instead, Midlands characters have to interact and react with Midlands, and when they go into a tactical adventure, they do so as part of the social forces in that world. In practical terms, in Season 1 of the campaign, they had support from the local baron and his men at arms, who guarded their base camp. They were a spear head in a siege and had the best weapons, armor and magical items, that the Barony could offer. This allowed me to have first level characters explore a mega dungeon that ranged in levels from 1 to 4 and featured 6th level monsters that fit the milieu.
I use all kinds of techniques to develop my adventures and my fantasy world. What makes my game D&D is Gygaxian Naturalism. This does not mean that I make detailed map of the huge tracts of wilderness. What this means, is that of the players have to go from Point A to Point B, to meet an NPC and try to find out some information, they ACTUALLY HAVE TO TRAVEL from Point A to Point B, and ENCOUNTER stuff along the way. This is what makes D&D a tactical game. You don't need miniatures or fancy sets to make the game tactical, the game takes place in the minds of the participants, and a good map can be drawn on a piece of scrap paper to help players visualize the situation.