i'll break it down for you, so even a worm can understand (jk):
* 2D Platformer.
not necessary, this is why:
* Non-linear level structure with backtracking,
whether you want to believe it or not, zelda 1's map is structured like this:
(image source: arne)
linear levels with branching paths and the like don't count.
the dungeons in zelda 1 suffer from this, but most of the game is non-linear anyway
* Levels are designed as a "world" rather than as a number of stages played in a strict order.
you can *beat* the dungeons in any order, if you have the necessary items. there is no set order, and you can even sequence break and get the white sword first, for example.
the only mandatory order is beating ganon's dungeon last.
* World may be split up into several large areas, possibly even connected by a central "hub" (a la Metroid Fusion).
i think if you have played zeldas, you know the world is composed by large areas
* Levels are also split up into individual "rooms" or "screens".
this is obvious if you have played the game, too. though it's not necessary as i pointed out in the previous page
* Permanent upgrades or items for the player character can be found.
blue / red ring, boomerang, etc.
* Some upgrades/items unlock new paths.
the boat/ladder, the cane to burn trees
in the end, what separates zelda 1 from the rest of the zeldas is point 2: the way the player can explore the world. in zelda 1 you can access almost every point of the map from the very start, without any need of new items. you can't do these in other zelda games, you always need "the flippers", "the fire tunic", etc.
also, another point to take note is that zelda 1 has no "errand quest". no one is asking you to RETRIEVE THE GOLDEN PLUME, or whatever. these kinds of quests (present in every zelda other than z1) make the game linear, and take away the freedom of the player.
another point i would like to add to the "checklist" is this, quoted from arne:
"Alternative routes - No absolute bottlenecks. Skill should be rewarded and allow the player to push ahead."
i.e., allow the player to venture more dangerous areas at any time (zelda 1 did this!)