Pre-research post with still-relevant information:
I think the reason Zelda feels more like an RPG where other games with the same or similar qualities don't is just because of the setting. The clear majority of medieval-themed games are role-playing games, so perhaps that's the reason sandel and I are inclined to classify it as such. Another part of it might be that the point of items isn't entirely to turn Zelda into a metroidvania. To speak of Zelda 1, sure, you've got the key items that are needed to solve a puzzle or traverse an obstacle, but the game is completable without better swords, shields, and heart containers; they're "level ups" awarded to the player for exploration. You could find some excuse to categorize almost anything as an RPG using similar arguments, I suppose, but "zeldalikes" share more significant qualities with RPGs than most others.
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Analytic post:
Personally, I recognize games as falling under one or more of these categories:
Driving - Driving cars or other vehicles, usually racing them, is a major part of gameplay. Examples: Need for Speed, Mario Kart, Burnout, Grand Theft Auto
Sandbox - A game where the player is meant to create his own goals within an environment with a minimal amount or significance of built-in goals, or the built-in goals are a means of achieving more significant player-made goals. Examples: Garry's Mod, Minecraft, Grand Theft Auto
Strategy - With the major subcategories of turn-based and real-time strategy and puzzle games. Strategy games are games in which tactics and planning are a significant part of gameplay. I personally consider stealth games to be a subgenre of strategy games for their tactical nature. Examples: Command & Conquer, Age of Empires, Fire Emblem, Bejeweled, Final Fantasy Tactics
Adventure - To qualify as an adventure game, a large part of gameplay should be finding and exploring large and interesting environments. The key concept is that rather than simply 'make it to the next level so you're closer to the end of the game', the environment has specific defining characteristics, nonlinearity being the one which stands out most. Metroidvanias are adventure games with the defining characteristic of finding specific items which grant abilities to the player to make reaching the next area possible. Examples: Ocarina of Time, Half-Life, Metroid, Castlevania
Action - Action games are won and/or played through directly fighting opponents. Though most games involve fighting, a game should only be considered an action game if it's the absolute primary means of progression. Shoot-em-ups and first/third person shooters are significant subgenres. Examples: Twisted Metal, Half-Life, Call of Duty, Cave Story, DOOM, Metroid, Castlevania, Deus Ex, Mario Kart
Horror - These are games that are meant to be scary or creepy. There's not much to describe for this one. Survival-horror is a major subgenre, action-horror is one common combination of genres. Examples: Resident Evil, Silent Hill
Platformer - A platformer game is one where major progression is made through maneuvering obstacles, most often platforms of some kind. Examples: Sonic Adventure, Mario, Cave Story
Simulation - Simulation games give the player control over a simulated environment. Tycoon games are one subcategory in which the player is allowed to shape the environment with the goal of making money. Sports manager games also fall under this genre. Examples: Sim City, Spore, Farmville
Sports - Sports games is essentially some sort of mutation of a simulation game, but they're generally set apart enough to warrant their own genre. Where the typical racing game is simply classified as a driving game, a NASCAR game would be both a driving and a sports game for that unique characteristic that sets it apart. Examples: Madden 'XX, Tiger Woods Golf, Tony Hawk's Pro Skater
Role-Playing - RPGs are characterized by having progression tied to the earning of more powerful exclusively offensive and defensive capabilities. Though it's not a mark of the genre itself, RPGs tend to be very story-centric, where the player is presented with a role significant to the story, as opposed to a simple 'rescue the princess' plot. Rougelikes should be considered a subgenre of RPGs. Examples: Final Fantasy, Kingdom Hearts, Fallout, Fire Emblem, Deus Ex
There are always games that find holes and create their own genres (Flower being the only one that comes to mind at the moment) but there will always be the odd ones out.
So where does Zelda 1 fall? I'd say it's an Action-Adventure-RPG. Combat with enemies and bosses is frequent and the means of acquiring new items earns its status as an action game. Some of those items (heart containers, weapons, shields) serve the sole purpose of making the player more formidable against his enemies, which makes it an RPG (what's the difference between grinding for stats and grinding for equipment? In many RPGs you do both.) and other items serve the sole purpose of making previously impassible obstacles open up for the player to enter new areas, which is necessary for progression through the game, thus its classification of an adventure game.
So looking back, I think Zelda 1 (and in fact, most "zeldalikes") should be considered to be an adventure game first and an action/RPG second. This also places them close to metroidvanias, most of which should fall under the same genres as Zelda 1 plus Platformers.
Well? It took me an around hour to research and type this post so you'd better appreciate it whether you completely agree with it or not