For me a Roleplaying Game qualifies as such when you're assuming the role of a character and have some input on how they react to events. There's a lot more restrictions on creating a character in the Fallout games as a WHOLE versus, say, the Elder Scrolls but I think it's still squarely in the realm of an RPG. Otherwise, the Witcher games wouldn't be RPGs and that's just ridiculous.
But unfortunately that is too generalized, by that logic most games could be considered RPGs. Super Mario would be a RPG, you assume the role of Mario or Luigi and decide which enemies to jump on when confronted with them, which blocks to headbutt, which pipes to go inside of, if you should get that mushroom or that flower, if you should try and jump the highest possible for the level end flag, if you go right or left, etc.
Again I say, grab all the RPG games from all the RPG genres (P&P, cRPG, jRPG, Action RPG, Tactical/Strategy RPG, First person RPG, Isometric RPG, Third Person RPG, party based RPG, solo player RPG, etc) and see what they all have in common:
-They all rely on how the character can use it's stats, skills, strengths, weaknesses, and personality to interact with everything and every situation in the game's world/universe. The world, it's people, it's obstacles, combat, speech, items, literally everything follows the rules that allow the characters (PC and NPC) to use their skills and shortcomings to surpass or fail challenges. Without those stats and skills, strengths and weakneses there are no RPGs. There is no doubt present that every single RPG has those until game distributors started to dilute what a RPG is (around early 2000's) because for some reason people who don't like RPGs thought it was cool to play RPGs and so they had to make games with some RPG features and call them RPGs for players to feel happy. Forget experience and forget leveling up, RPGs do not necessarily need those to be RPGs, forget choice and consequence, forget good stories, forget special abilities too. All a RPG needs is the stats and limitation on characters and the world to follow the same rules.
What you seem to call RPGs are games where you don't always have those rules and skills and stats and limits but where you can pretend in your imagination that you are that character and that is not a RPG, that is way more akin to LARPing (which is people pretending in their heads they are this character and behave like it). Imagination =/= RPGs, while imagination enriches the RPG genre it does not dominate it.