You mean Dragon Quest and Final Fantasy? Yeah, they played like LoZ alright ..... e_e

How are they proof when a game that had the very same elements, but was not an RPG was released in the same year - Kid Icarus (December 1986) vs. Final Fantasy I (December 1987) vs. Dragon Quest (May 1986.) 

The elements emerged as analogies in these non-RPG's. Kid-Icarus didn't take its elements from RPG games, they were design choices for the games. The same is true for The Legend of Zelda. 

Even if Kid Icarus and TLoZ took their inspiration for these qualities from Role-Playing Games, how does this bolster your point? Kid-icarus had just as many "rpg elements" as LoZ and it still wasn't considered an "action RPG." Elements in TLoZ that weren't found in most console RPG's at the time: 1:1 button-mapped controls, puzzles, all enemies in an area must be defeated before progressing in certain screens, scale remains constant, weapons are upgraded rather than exchanged, items affect environment (bombs, for example), and I'm sure there are a few other differences I am not remembering. There were no towns in TLoZ. There was no skill customization in TLoZ. There was no leveling system in TLOZ. There was no loot system in TLoZ. TLoZ took primarily from two genres, the Action genre's gameplay - real-time combat from screen to screen, and the Adventure genre's exploration, inventory system, and puzzle elements. It also added a few new elements of its own, such as open-world gameplay, for example. Hence, it was (and is) an Action-Adventure game. 

In a weird way your totally right.  I usually think of mechanics of an rpg taking place from the beginning of a game to the end, but yeah; there's nothing that says it can't happen during multiplayer.  

RPG = Role Playing Game = Game in which you role play

Zelda gives you a pre-defined character that's fully controlled by the story. You don't get to do any role-playing. An experience system, although commonly used by RPG's, does not automatically make a game an RPG so Zelda II shouldn't be counted as an RPG either.
I now this also makes most JRPG's non-RPG's but that's why God gave us the JRPG genre, so we get to call RPG's that really aren't RPG's, RPG's.

There are many required mechanics in an RPG that Zelda does not have:
1. All RPGs must have an experience point based system and levels.
2. Combat is based around stat calculations and turns, an action RPG simply converts these into an action based execution which impacts combat. I.E. Strength modifiers,
3. All RPGs must have some sort of stat based progression, like strength, vitality, wisdom, and dexterity, which go up as the character gets more experienced.

The reasons why "you play the role of Link" is a terrible definition of a game genre is because it doesn't describe any gameplay mechanics, it is also not at all specific, and would include just about every game from dr. Mario to Pac-Man to Doom. RPGs are specifically about the gameplay mechanics used to design the games, they are primarily adapted from the pen and paper game Dungeons and Dragons. Zelda does not fit the definition of an RPG, not even close, it is in fact an action adventure game, and the point is no more arguable than the existence of climate change; no matter how much you want to deny it, it does factually exist.

Best describe for Zelda is Adventure game.

It is an RPG to me.
You role play as Link and immerse yourself in his day by day life.

It is slower paced, with focus on puzzles rather than heavy combat.

Perfect answer.