Setting hyperbole aside, D&D5e has the potential to be resource management heavy, or light, depending on how you run it. It has the potential to be exploration heavy or light, depending on how you run it. It has the potential to be combat heavy or light. Story heavy or light.
It's a great rule set. There are other great rule sets, too. This one leans more towards resource management, though not quite to the extreme of say, Pathfinder, or Call of Cthulhu. At the opposite end of the spectrum you have games like Dread and Fiasco. There is room for lots of approaches.
What I take OP to be asking is "is resource management a defining feature of D&D?". In other words, could you have zero resource management and still recognize what you are doing as D&D? I would argue not. Ultimately, I think hit points, spell slots, and combat rounds with resources such as movement and actions are defining characteristics of the game. Other resources, like inventory, are not essential, but those basic resources are part of what make D&D, D&D.
Edit: RPG is a much more general term, and I think the defining feature is literally in the name: role playing game. It has to have a story in which the player is an active participant. It definitely does not require resource management; there are plenty of RPGs that do not.