You argued that any game can be an rpg if you slap some additional layer of mechanics onto it, but the term itself does not describe any concrete mechanics that are mandatory for an rpg to be an rpg.
I suggested that stats are one of such mechanics, so in fact the term
does refer to something specific. Of course stats alone don't constitute an rpg and not any game with stats is automatically a
role playing game (like some shitty soccer or COD multiplayer). There are other things specific to rpgs, such as the aforementioned focus on the player character(s) progression, which would be impossible without stats representing various aspects of said character(s), no matter in what form (numerical or not). In other words: stats are not like an air conditioner that you can remove and have, less comfortable but still, a car.
RPGs are a genre of their own and as in case of any other genre an rpg is just a sum of respective elements that can be shared by other genres as well. RPGs simply don't have one specific form of gameplay, but then again, what genre does, or is explored enough for such conclusion to be valid?
Yeah, try beating Deus Ex the shooter way, by killing everything on sight. It's fucking Doom with additional layer of mechanics, R00fles! You either gonna get killed or run out of ammo in minutes.
Oh look, it's Wolfenstein!
tldr; Crawl back under your rock or climb one in your shitty Skyrim you silly green lizard; that game is indeed a shooter with some additional layer of mechanics slapped onto it.