Sorry Lacrymas, your definition of RPG is completely arbitrary.
This is the most importent sentence of the wiki (regarding this topic): "Although some single-player role-playing games give the player an avatar that is largely predefined for the sake of telling a specific story, many role-playing games make use of a character creation screen."
The artice does not divide RPGs in 2 different groups. There is simply the fact that different games have different freedom in character creation.
There is no difference between arcanum, fallout (RPG RPGs according to you) and D:OS1 (Self insert RPG according to you). You can freely create your char(s) in a system without classes. They have a background (airship crash survivor, Vault dweller, source hunter) and a goal (save the world).
In PST you are limited to a male human who starts as fighter and has no dump stats, but you have still many different ways to play him.
I consider the terms "RPG", Action adventure", "FPS" and so on are abstract concepts that will never be difined precisely (There will always be people who find arguments against a specific definition). Each real game exist in a continuum and follows some of these concepts more or less. Most games have elements of several of these concepts. Some games (like deus ex) are so hybrid, that pushing it into one genre will never describe the game completely.
From my point of view, D:OS is as much RPG as a game can be.
Prof. Dr. Dr. Mad S. Tist
World leading expert of artificial stupidity. Because there are too many people who work on artificial intelligence already