It's just a matter of opinion... most time, when we say "metroidvania", we don't talk about a genre, but about the game's mechanics, being a "metroidvania" implies that you'll have some sort of open map you can travel the way you like, only you'll be blocked at some point until you got the good power/item to go farther and open new areas and shortcuts to previous areas.

And as the "Metroid" series and later "Castlevania - Symphony Of The Night" are the games that popularized those mechanics, that's why we've called that "metroidvania".

And to be honest, I've never heard about a "shoot & run" genre, and I play since the mid-80's (then, I'm not english or american, but the names of the genres are pretty much the same here in France)... I know "shoot'em up", or "run & gun", but HK isn't quite a R&G (R&G are games where you run and you shoot, like the "Contra/Probotector" series, or the "Metal Slug" series).

HK is an action/platformer, with "metroidvania" mechanics, and it's an OBVIOUS tribute to the Metroid games, so, nothing fits better than "metroidvania".

Sorry, but "ShootNRun" doesn't quite describe HK, you don't really run, you don't really shoot... "metroidvania" tells you exactly what the game is about... your description somewhat reminds me the "Turrican" games, which hold a vague ressemblance with "Metroid", but it's not quite the same thing, "Turrican" is more a kind of opened-map shoot'em up, but hasn't the exploration factor of the metroidvanias.

If you tell me "ShootNRun", the first thing that comes in my mind is "Run & Gun".

Then you just seem to not know what you're talking about the NES... the NES crushed the world market, it only tied with the Master System in some countries (like France) where the NES had a really late release (sometimes even after the Master System), here in France, both machines came out by the end of 1987 (the Master System first was utterly dominant, but by the early 90's, SEGA abandoned the MS to promote the Megadrive, and the NES became the cheap alternative for those who couldn't afford a Megadrive or a SNES, and began a second life, leading to more consoles sold than the MS at the end), in Japan, the NES was released in 1983, and in 1985 in USA, and there wasn't any strong competitor.

And you know, it's not always a matter of who comes first, "Doom" wasn't the first "FPS", "Wolfenstein" was there before, but before the "FPS" term was popularized, the genre was simply called "Doom-like"... not because it was the first, but because it was the one who popularized the genre.

There is. It's recognized by everyone here but you.The term you are looking for is "run 'n' gun". "ShootnRun" is not nor ever was recognized as a genre name. And no, just because a game is a 2D platformer does not make it run 'n' gun.There's a major difference that Metroid is recognized for - exploration of an interconnected map and acquisition of abilities that in turn advance your exploration. Patently wrong. All entries from both series on GBA used the Metroidvania mold, as did all Castlevania titles on the NDS. And, of course, we can't forget Symphony of the Night on PSX.And here's one more error on your end... Metroidvanias as a rule of thumb do not have "level length". While distinct areas within the map do exist, the key element of the genre is exploring a large, interconnected map. Which Hollow Knight does.