What the heck is a "Pure RPG"?
Trick question. There aren't any.
*Waits for the audible shock of outrage to die away*
Ready to listen? Good.
Let us look at the word. Role-playing game. Hence, any game where the player takes on the role of a character. That means most of them. Zelda, Mario, Metroid, Halo, Uncharted, Tomb Raider. These are all role-playing games.
This means that games like backgammon, checkers, maybe simulations like the Sims or flight sims, but that's sketchy.
But I can hear you saying: "But, Inkidu. RPG defines what one does in a game not what one controls!"
Lets look at Baulder's Gate or in fact Dungeons and Dragons.
These games' playing mechanics don't rely exclusively on the player character. You could call Baulder's Gate a tactical real-time strategy game (I've never actually played it because I've never been able to get into DnD) it relies on pause-and-play game play.
DnD on the other hand could be seen as a turned-based strategy. Players take turns moving and preforming actions. Both these example rely on what kind of character is created, but they're hardly purely based on role. There are a slew of other elements, but the mechanics are not purely determined by your character, your character is determined by mechanics.
Conversely, Legend of Zelda. You the player, step in to the one-size-fits-all Kokiri boots of Link (or what name you will). You are tasked with reuniting some crap somewhere and along the way killing lots of minions and a giant pig wizard. Now, link grows and develops as a character he gains items and hearts. He thus levels up in a way being able to take more damage and do more things with the items he's plucked from the cold, dead hands of his foes.
So while I'm happy to accept the moniker of RPG as a descriptor for a style of stat-based, grinding, loot-hoarding, genociding rampage across magic land. One must admit that every game has some kind of role-playing element, and that I'm not basing this on pure semantics.
It's like survival horror. The goal of most games is to survive, the horror aspect is just what the larger portion tries to do.