A game in which you portray a living being and in which you can affect one or more actions taken by that living being.
That would put any game on the spectrum, in any case.
Yeah, that pretty much means most games ever made, it would be harder to find games not fitting that description. Pong? (Although you argue the "racket" is indeed a living being or at least controlled by one…)
"A role-playing game is a game where you play a role". Umm, well yes, that's actually true I suppose.