You mention another's life (or do you mention another ~second life). You mention skills as being artificial, then mention 'things you can do', and "stuff that measure how good we are" (in game).
If you mean another's life... then I agree. It is a role ~like Hamelet, or even like each character in Voltron, or any character in a novel... Or even one where you decide much of the character yourself.
With this sort of other's life, you would want to know what that other spent their time learning (and how good they are at it).
If instead, you mean a second (virtual) life ~of your own... as in "I get to be a wizard", then I agree that you don't need much in the way of stats & skills, but I don't see that as a role playing game... There is no role. I see that as an action adventure akin to super mario (he can run, jump, and shoot fireballs too).
I disagree again.
I dont see warrior, theif, or mage as roles. Those are classes. Skills show if you are good or bad at something, and they measure the progress as you go from bad to good. An novice of magic is just as much a mage as the master mage. The master mage could put the novice to shame, but they're both mages. The role for me, is what kind of mage you are. What kind of theif you are.
Mario may be able to shoot fireballs, but he can only walk forward. His path is clear. That's why Mario isn't an rpg. A mage in an rpg could be good, evil, or grey. They're path isn't clear, and only after they make the choices in the game do the paths begin to show themselves. If Mario could somehow choose to be evil, good, or some where in between, then i would consider that game an rpg, even if his fireball never gets stronger.