I define a roleplaying game as any game where (1) players control personal avatars existing in a fictional milieu and (2) said avatars enjoy some degree of tactical infinity, which is in turn defined as the capacity to attempt any conceivable action, constrained only by the fictional positioning and not by the game's mechanics.
Put another way, if the player can say, "My character does (reasonable thing x)" and there's a way to resolve (reasonable thing x) that isn't necessarily specifically covered by the rules, you've got an RPG on your hands.
D&D very obviously fits this definition, as the definition was constructed to include everything shy of a free Kriegsspiele that isn't also a Braunstein.