...
Honestly.
The definition of the game is action/adventure. (or at best, action RPG).
But everyone being so nitpicky about what constitutes an RPG should go back to basics.
Stats do NOT make an RPG, let alone grinding.
Story and character progression make an RPG.
Your character improves with time, and becomes more powerful.
Wether this is due to fighting alone, or something that makes sense in context... (Several pen& paper RPG's reward experience based on how well you got through the story, not your ability to fight monsters.)
So... Zelda...
Well, you get stronger as the game progresses, and it has a story which is a major focus of the game.
Also... (and this is amusing if you get into the history of D&D), you spend most of your time wandering around Dungeons.
By the definitions that RPG's started with, it's close enough.
It may not be what is generally thought of as an RPG computer game, but it has the main elements that define RPG's generally.
Turn-based combat is, after all, a contrivance born of necessity, and not at all required for a computer game.
It has a definable progression, based on known goals within the game (you gain 'hearts' primarily through completing dungeons - Eg. You get stronger, or 'level up')
It also has a lot of superficial tropes related to the RPG genre (which you'll notice with JRPG's), for instance, the NPC's in villages, and things like that
I notice some people bring up Metroid as a comparison; While it's certainly true that they are very similar in style (or at least, used to be) - There is a notable lack of any significant story elements there...
Metroid might have an intro, and an ending, but beyond that, it's really just you and the environment.
Zelda has a lot of people to talk to, and far more structure and context to what you're doing than the older metroid games ever did.
So... Bottom line, Zelda is not an RPG by the definitions of the computer game genre, but by the wider defining characteristics of RPG's, it is pretty close to one.
If you don't agree, perhaps you need a wider perspective on just what an RPG actually is...