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.
I don't think anyone has said "The game can be completed in any order." as a quality of a Metroidvania. Sequence breaking exists in a lot of Metroidvanias, but by and large it is not something explicitly put there by the designers. I certainly wouldn't claim that sequence breaking is required for Metroidvanias.
Also, no one said that linearity couldn't exist in a Metroidvania. Every Metroidvania is linear to some degree (again excluding major sequence breaks), it's just that the linearity isn't obvious to the player and feels organic. It isn't "You need key 5 to get past this door" it's "Hmm...there is a ledge up there that I can't get to, if I can ever jump higher, I'm coming back here."
And there is an errand quest in Zelda 1 (if I understand your idea of an errand quest). You need to collect all of the pieces of the Triforce to complete the game (excluding extreme sequence breaking).
And if metroidvania doesn't imply a 2d platformer, then I think a term to specify a 2d platformer metroidvania needs to be thought up. I nominate Metroid-like.
I guess this is probably a matter of personal taste and I'm not sure that there is a definition that will be satisfactory for everyone. Let me use my favorite definitional argument as an example.
A: What is a sandwich?
B: It is 2 slices of bread with toppings in between.
A: What about a submarine sandwich, that is only 1 piece of bread with toppings in between?
B: Ok, it is 1 or more pieces of bread with toppings.
A: Ok, I'm going to go get a sandwich, do you want one?
A returns with 2 hotdogs
B: What the hell. That's a hotdog, not a sandwich.
A: By your definition a hotdog is a sandwich, so enjoy your sandwich.
The point is, by every definition of a sandwich that doesn't explicitly state that a hotdog isn't a sandwich, a hotdog is a sandwich. That being said, no one imagines a hotdog when they think of a sandwich. Similarly, except for the matter of perspective Zelda is a metroidvania, but I feel you have to be pretty disingenuous to say that if someone said, "I'm making a metroidvania" you would think "Ooh, that's going to look like The Legend of Zelda."