Not really.
In Pokemon you are specifically playing the role of Red/Leaf, Ethan/Kris/Lyra, Brendan/May, Lucas/Dawn, Hilbert/Hilda, Nate/Rosa, Calem/Serena, Sun/Moon.
In Mario you play as Mario.
In Legend of Zelda you play as Link.
In Luigi games presumably you play as Luigi? In all honesty I have never played one of them though.
In Jak and Daxter you play as Jak.
In Daxter you play as Daxter.
In Halo (campaign specifically) you play as Master Chief (except for one part where I believe you play as Arbiter, I don't remember to be honest?).
Like @jcsnider said GTA 5 is filling a role as well.
In Monster Hunter you fill a role.
In Blade and Soul you fill a role.
In Final Fantasy you fill a role.
In Kingdom Hearts you play Sora/Roxas.
Regardless of classification in all of these you fill a distinct role, for MMORPGs is slightly more nebulous because you customize a bunch of things, but the role-filling is still the same.
Roller Coaster Tycoon, Sims, Civilization and Europa Universalis are all not RPGs because you are not filling a distinct role, defining "distinct" as being an exact character, in the form of Mario and Link, or "the protagonist" in Blade and Soul and other MMORPGs.
League of Legends is also not an RPG because there is no story, and "role" is not specific to a character, it's specific to a position of play (i.e. bottom lane, top lane, goalie, midfielder, quarterback, catcher).
Regardless of what argument you make Mario is the textbook definition of playing a role, even though the game's medium of play is a platformer.
Platforming is a world/navigational mechanic, as are arena, open-world and sandbox.
Role-playing is in reference to story telling, and if a game has neither a story nor a plot it is not a role-playing game.
Shooter is a combat mechanic.
First-person shooter is a navigational/display/combat mechanic.