I can't quite see what point you were trying to make here. Also, there are plenty of games that fit my definition of an RPG; most Bioware games prior to KOTOR for instance or Black Isle's games from back in the day (Fallout, Fallout 2, Icewind Dale etc.).
To be fair, even those games aren't RPGs according to your definition. You can't decide NOT to go on the adventure for example. Eventually you're going to reach a predefined goal and beat the game.
The CLOSEST thing to a true RPG is MMORPGs. You create a character and do whatever you want. Some do this better than others of course, allowing you to either go fight, quest, and beat dungeons, or literally do nothing else but farm (Like, farmland) or make goods and level up that way.
But on to your initial point, a role-playing game is as such, as Ace Gunman said, you play a role. Whether this is a role you make or a pre-designed role does not change the fact that you are playing
A role.
Let's use FF7 as an example, if you decided to just sit Cloud at an inn and never leave, you're not playing his role anymore since it isn't in his character to do so.
The same applies to custom made characters. If you designed a character who is fearless and laughs in the face of danger and then decide to run from a fight, you have failed to play his/her role.
In this case, yes,
every game could be considered an RPG. Alas, the video game definition is different. RPG simply means that there are levels and stats and such in the video game world. If you think this is silly, then consider that most games could also be classified as action games or puzzle games and so on.
Anyway, that's my rant, and my opinion, feel free to think whatever of it.