I think simply defining it as "stats games" is too vague.
Yes, that's why I didn't say they are just stats games:
RPGs are stat games, where the characters have to use their skills and attributes to interact with their world. The player is the decision-making of the character and the character tries to act on these decisions.
The stats defining what your character can or can't do is the "foundation" of the RPG genre. If you analyze all the RPG subgenres (cRPG, PnP, jRPG, tRPG, aRPG) you will see that many times this is the only thing they all have in common (and it's the thing that makes them all RPGs).
Gaming genres are dependent on their "foundations" and then other elements are added to the "foundation". A gaming genre is only designated by the entire game, not just individual elements in the game.
For example, "Football Manager" games are full of stats and the characters actually use those stats to influence how they play each match. You play the role of a manager and manage your club, decide training schedules, hire staff, upgrade your club's stadium, hire and sell players, get friendly matches, decide your team tactics, make substitutions, give pep talks to your players, attend press conferences, etc. These games could be considered a RPG, but all of the elements that would make it a RPG are mixed so much with the whole sports manager "foundation" and elements that in the end, it ends up being a sports management genre and not a RPG.
Crusader Kings games all have thousands of different characters, all with their own Attributes and abilities, those attributes and abilities are used for pretty much everything in the game, including decisions that the player can have during events. It's more of a RPG than most modern RPGs. But it's a grand strategy game. Because mixed with the RPG elements is the grand strategy game "foundation" and other elements that obviously makes it a GS game instead of a RPG.
If you remove the character being the one doing things (using it's abilities, skills, attributes, etc.) instead of the player, you totally removed what makes a RPG a RPG. It stops being a RPG right away because that is the "foundation" that makes the RPG genre.
If you imagine any RPG ever made (including any sub-genre) for consoles and computers and remove from those games all the stats, skills, perks, attributes, and any other similar thing that is used for the characters to interact with their world. You end up with a totally different game genre that already exists.
Do that to the classic Fallout games and you would end up with a game that can be considered a bullet-hell-lite or isometric shooter with dialogue. Do that to Daggerfall and you have a FP Action game. Do that to Fallout 3 or FNV and you have a FP/TP Shooter. Do that to Planescape:Torment and you have a Isometric Interactive Novel
.
Why is that? Because without that "foundation", the games stop being a RPG.