Even if Metroid Prime/Other M changed a lot, they still kept the metroid feeling, (other m slightly less in some parts) but it still features a non-linear structure, the same can't be said for the other games.
Also about Assassin's Creed, the only items you aquire are the items you get when you Assassinate the targets, and you restore your rank. There are no other pick-ups in the game. There is more to item pick-ups in metroid than just what you get from the bosses.
Also as for in the first Assassins Creed, you didn't have to use the throwing knives or even the sword. However, you still couldn't progress to a new area without getting the items.
This, the same could be said for a lot of other games.
i would argue for that Batman Arkham Asylum has limited platforming aswell, i mean you can climb in Splinter Cell games, but you wouldnt classify that as a platforming game would you?
They're just handled slightly differently because its no longer a 2D pure platformer game, but now a 3D game.
this same could be said for the 2008 Prince of Persia then?
it features an open world, there is platforming, there are puzzles, and there are power ups (Elikas abilities) that let you reach areas you couldnt before
Another game Crackdown somewhat fits in the same formula. You have platforming, there are no puzzles but like Castlevania it has RPG elemets. It's a free roaming open world game. And powerups/pick ups are handled slightly differently.
To be able to progress further in the game you have to make yourself stronger, find new equipment that improves you (similar to most Metroid-eqsue games) and new weapons that help you tackle the rest of the story (again like metroid). The game is quite open, as in you could go anywhere right from the start, but whats suggested is to take out the Los Muertos first since they are weaker and everytime you kill a boss, you can pick up his weapon, a lot of the times the bosses carry new types of grenades, usually stronger ones that will make later boss easier, as in let you progress the story. Other times they carry grenade launchers/rocket launchers. Again items that will make the following bosses be easier, to be able to progress the story.
2 other games, Darksiders and Okami, which by everyone is considered some sort of Zelda-clones. Could also fit this category, I haven't personally played Darkisders but from what i've seen, heard and read, it basically Zelda games that is more combat oriented similar to God of War, but again i haven¨t played it so i might be wrong.
Okami on the other hand i have played, it too is compared to Zelda games, but it could fit in to the metroid category, based on some of the criterias.
It has an open world, which is free-roaming similar to the other games i've mentioned. It features platforming and puzzles, combat is not the main focus of the game. It has exploration and most importantly it features power ups (brushes) and equipment (the weapons, Beads Reflectors and Glaives) that you get once you complete certain things in the game,
With some of the items you can't progress without them, mainly the Brush techniques, but also some of the weapons. Snarling beast ( a reflector, one of the round-shield like looking weapons) for example which you get from the first boss, you can't progress through the game without it. From some of the criteras it does fit a metroid like game, but most people would argue that it is more of a Zelda game.
Like you mentioned Zelda games are pretty hard to define, some call it RPG, some call it Action-Adventure, but by some of these things i've mentioned it does fit with the metroid category. But no one would call a Zelda game metroid-like
I just think your criterias for what a metroid game is, is a bit too loose, or wide. Not specific enough.
Like people calling Metroid Prime a First Person Adventure, then what are games like the myst series and other similar games?. Should Uncharted be called a Third Person Platforming Shooter? i mean it has platforming and it has shooting, it controlls from the third person. Compare it to Gears of War that has no platforming (not sure on this one, haven't played it enough)
San Andreas had RPG like elements with the building up your characters skills, should it be called Third Person Shooting RPG? Is mass effect 2 a shooter, or a rpg? It's been a while since i've played mass effect 2, but i felt that it was a bit more linear than the first one, and the shooting mechanics had been improved while the rpgs elements of the game were trimmed down.
Also i'd argue for that Infamous is just as much a Platformer as GTA is a racing game
Again as you mentioned a lot games could fit a lot of different genres because of some element in their gameplay. I still think its important to really distinguish games that are metroid like from games that are just action or adventure.
here is a list of some metroidvanias
http://tvtropes.org/pmwiki/pmwiki.php/Main/Metroidvania
some of the games i've never heard of
here is another http://www.listal.com/list/metroidvania
