Personally I've always thought that RPGs were best characterized by a system of stat/level growth. A player's characters would almost always begin a game in a fairly weak state and would be unable to handle all but the most basic and common enemies. However, over the course of the game -- and especially as a result of the player's actions and direct commands in battle -- the player's character would be gradually transformed to be able to fight progressively more difficult enemies. Therefore "control" in the sense of telling a character what to do still relies on a certain degree of player skill that is comparable to any other game.

The difference in my interpretation of an RPG from say, leveling up a weapon in Castlevania or Super Metroid, is that these other games focus on improving equipment but not necessarily the player's character. Therefore, growth becomes less individualized in the context of these other games as the player cannot change fundamental aspects of their character, limiting the degree to which a player may actively engage in "role playing" . Of course there are many exceptions to this rule, and genre boundaries are routinely blurred making the whole business of defining the critical elements of an RPG somewhat difficult... To side step this whole issue, I simply think of RPGs (or RPG-esque games) as having some form of stat/level growth. :p

Finally in regards to your last question... I can't think of any game in which a player might engage in a system of turn-based combat without actually experiencing the rewards of stat/level growth. Heck, even strategy RPGs rely on some form of character growth to improve a player's units over the course of the game.