So - is Super Mario an RPG? Does eating a mushroom, fire flower, or star count as equipment / stat bonuses?
What about a racing game, where you get cars with more horsepower, stiffer suspension, etc. or other "equipment bonuses"?
These are great examples which, honestly, I've never thought about as possible rpgs before.
For super mario, I would like to say it isn't an rpg, but I've barely played the 1st or 2nd game for the old game boy (the big one) so I can't talk about the whole franchise. My reasoning is that the equipment/power ups that you mentioned, are usually too limited either in duration, maps, or uses to force the character in a specific and defined gameplay loop.
Now racing games, in my opinion can be rpgs with each car fullfilling a different role. Being able to change cars does negate most of limitations of having a rigid role, but still each car has a playstyle and race types were they excel and others were they don't. With that in mind it's up to the player to either roleplay a single character/car or not.
How do you have a game that doesn't depend at all on some "ability of the player" even if that ability is... configuring the stats? Yes, I'm asking if auto-battlers could be considered as having RPG elements in this context.
Short answer: You can't remove the player's ability.
Long answer: It's a game not a 1-1 function. Even in the same rpg, with the same characters, two different players can and will take different actions at some point and that might affect the outcome.
I don't know what an auto-battler is. I might not have been clear on my take in my previous post, but I believe an rpg isn't about the stats by themselves. It's the mechanics and their effect on the gameplay options that a player might have. The character's stats are just a representation of their "abilities", in other words of the mechanics they can or can't use. And it's important for an rpg to have mechanics that are exclusive to certain characters, otherwise you don't play
a role, you play all roles and that's defeating the point.
Some examples:
In NFS:Underground 2 (iirc) you can have a car that has great top speed and acceleration but poor control/handling. So when you came to a corner you had to hit the breaks a lot or you'll hit the bars and lose control,time etc. That means that on maps with lots of corners you were on disadvantage and you might want to avoid them, which you could to some extent.
Again in the STALKER games, a character with good radiation/anomaly resistance could go through anomaly fields in order to attack or evade some enemies. Or had to run from certain enemies because their high recoil sniper rifle is a bad weapon against small and fast creatures that like to swarm you. Or they couldn't even run because they opted for a weapon or armor that disabled the ability to run.
And to give an example of a "bad" rpg design, vanilla Skyrim, where each and every character is expected and quite often forced by quest design, to do everything in every run (join all but maybe 2 guilds, do all quests, learn all the shouts, maybe learn all spells).