What constitutes an RPG?

...No. Static or not, it doesn't matter. A RPG can be very linear without much randomness.

It is the focus of the game. An adventure game put emphasis on area such as puzzle solving and adventuring. For example, the Silent Hill series. But there is indeed a lot of actions in many adventure games, so personally I don't mind people calling a Adventure game as an Action-Adventure... But Adventure-RPG? No. Not unless it does have RPG elements in it. (Upgrading or finding weapons isn't a RPG element, by the way.)

Just in what games are you NOT playing a role of something? (Pong, Minesweeper, Tetris... you don't have to answer this question.) Well, even in the Gran Turismo series, you are playing a role of someone. Or the Championship Manager series, where you are playing the role of a Soccer Manager. In fighting games, you are controlling the characters you've selected, and play his role during the fight.

Just because we get to play a role of something in a game does not make it a RPG game.