The core of an RPG game is an RPG system of rolled challenges versus skills/level/stats. Then layered on top of that is everything else that is typically something from other games. Some people will say story. But story without an RPG system is an adventure game. Some people will say combat but combat without the RPG system is a tactical game. Some will advocated for more simulation like gameplay, although this one is probably more modern it does harken back to some Ultima style stuff.
Most Old School cRPGs have a significant amount of both of those or in the case of some roguelikes; just the combat part. Therefore most people tend to identify that both of these are part of the "core" of an RPG. But they are not in reality as we have classic example of cRPGs that lack either one. Personally I am fine with a pure dungeon crawl with negliglible story and I am fine with a game with a great story and a only servicable combat system.
The only thing that can really be said reliably is that the core aspect of RPGs, the rolling/advancement/gear systems are never standalone because they are incomplete or at the least have too little meat on the bone.
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I would say it would probably be best to simply stop using RPG as a genre term entirely. I would say this as the RPG aspect is not really a standalone genre rather it is essentially a sub genre of many other genres and or hybrids. It is no longer even the case the "classic cRPG" is in the majority of game and the term "classic" is misleading anyway due to game like Rogue which certainly a classic on the RPG scene.
So what we have is people with varying preferences for OTHER genres saying an "RPG" is a bad RPG because its not a good representative of a different genre they like. This is just people saying the same thing in confusing ways because its all essentially defined in contradictory ways.
Some people who like Adventure style gaming and have a little care about combat or are able to tolerate OK combat will say games like Arcanum or Planescape are great RPGs. In reality they are saying they are great open ended Adventure oriented stories. Others who demand good tactical systems will say those two games are mediocre RPGs, but are really saying they are medicore tactical combat games but automatically fold this into the idea of what a "classic RPG" is. Compounding this to make it even more confusing is the RPG systems themselves since a poorly designed system can make the combat or the adventure gameplay seem considerably worse and people often don't separate this, i.e. for example overpowered RPG builds can make the combat system appear much worse than it is or poorly designed lockpick can interfere with adventure gameplay etc etc.
Wow you wrote a lot!!! I almost didn't read, but I forced myself.
I see what you're saying.
The central problem is the CORE--which you define as rolled challenges (like dice) versus skills/levels/stats--is almost nothing on its own, as you also point out when you say it's "incomplete or at the least have too little meat on the bone."
So RPGs add things to the CORE, but those things come from all of the other genres, causing all this confusion.
I would argue the reason the CORE exists at all is because we're supposed to be playing another character which exists in anothe reality. That character has stats/skills/levels, represented as numbers or floating point in program code. When we perform an action, those stats/skills/levels are factored into the outcome of the action. This happens because we're playing that character, not ourselves.
If there were no stats/skills/levels, we'd just be playing ourselves, right?
But is that really true? Are we really just playing ourselves if the character we're playing in the game has no stats/skills/levels? I don't think it's. I know the codex unanimously disagrees. Or at least lots of em disagree. But I believe those things aren't necessary to roleplay. I never needed them when I was a kid rolepalying batman or gi joes. All I needed was a furtive imagination fed by lots of background on the character(s). I can roleplay a thief without that thief having stats/skills/levels. I can even learn and become better at being that thief by acquiring knowledge and improving MY skills in that game. That thief can have a name and a history completely separate from my own. I merge with that thief and we become two people in one.
The problem is if I define RPGs as just merely roleplaying an archetype or character--without any systems of stats/skills/levels behind it--then many Adventure games and others might possibly be classified as RPGs. Even mario brothers might be classifed RPG, since you're technically playing Mario, not yourself. But nobody is going to accept Super Mario Brothers is an RPG.
So I have to agree with you for the moment, although it looks like you're saying RPG shouldn't exist as a genre. And that I find hard to agree with. RPGs do seem distinct to me in that their worlds and characters are usually deeper than adventure games. The interaction with the world, characters and story is also deeper. Choices and consequences! You can replay RPGs more reliably since they're made to be played by multiple different roles or archetypes.
It's like hte features of an RPG are there to remind you that you're roleplaying a character in another world. And it's not something done lightly. RPGs go out of their way to make you think this. It's the objective.