Oh no, MrMen, you’ve wandered into the realm of Game Genres. Welcome to my nightmare.
High Level:
“Classical” definitions of RPG:
A game where you control a character or a party, including experience from fighting/doing objectives, leveling, quests (main or otherwise), and an overarching narrative. Usually with a full equipment system, and some kind of turn based or tactical combat.
Example: Final Fantasy, Dragon Quest, Ultima, Eye of the Beholder
Action RPG:
Take the majority of the above (not necessarily all), but make the combat direct control and not turn based.
Example: Diablo, Kingdom Hearts, Dark Souls
Strategy RPG:
Take almost all of the standard definition, add some form of controlled movement, usually a much larger number of controlled characters.
Examples: Disgaea, Final Fantasy Tactics, Troubleshooter, X-Com: Chimera Squad
However, these are all loose guidelines, and there’s probably thousands of permutations.
For your questions: Is a dungeon crawler a type of RPG? Sure! A good example would be Eye of the Beholder. Thats 100% an RPG and a Dungeon Crawler, even though it’s almost EXACTLY the same perspective/set up as Might and Magic, despite Might and Magic having an open world as well.
Most people are conflicted on the Zelda games, though. Zelda 2 (Adventure of Link) is absolutely a side scroller RPG as it has most of the main definitions. The Legend of Zelda, and A Link to the Past, are viewed much more as Action Adventure games rather than RPGs.
However, most people DON’T view, say, Simon’s Quest (Castlevania 2) as an RPG, even though it’s near identical to Adventure of Link. I don’t agree with that viewpoint (I think Castlevania 2, Symphony of the night, and the millions of Metroidvanias with equipment and leveling, are all RPGs), but that’s me.