It's like when fanboys tried to force "first person adventure" tag onto Metroid Prime to excuse Gamecube controls, or when that PS2 abortion Chaos Legion was called an RTS. It's done to distinguish whatever game you like from other similar games, and possibly to deflect some common criticism. Who cares that the game is less than an hour long and you mostly fight the same enemy over and over? That's a character action game tradition, you are supposed to play it again on modes that bloat that same enemy's stats by 50% and 100% after that.
Though in case with DMC and Platinum games it's mostly done to isolate a subgroup of action games that play similarly. If you made a thread saying "I just bought DMC5 and all of its pozzed microtransactions and I love it, what other action games do you guys recommend?", you probably wouldn't like it if someone suggested Spider-Man, Ni-Oh and Dynasty Warriors 9. I guess that this subgenre's definition becomes a little too loose if you include God Hand and Ninja Gaiden under the "character action" umbrella. And you can't even use "depth" and "quality" as the genre's defining features when Gungrave, Shinobi (PS2), older God of War games, and even Ninja Gaiden 3 are also supposed to belong to it. But even then, some common elements are still there - an at least moderately difficult action game that you replay over and over, that has a meaningless counter or gauge that goes up as you whack enemies, oh and the plot is ridiculous.
The name is stupid and insufficient, as is CUHRAYZEE that I love, but so is probably any other attempt to accurately describe these games in 1-3 words. This is hardly the first time a subgenre or even an entire genre got an ill-fitting name, so I find it difficult to complain here. Just look at requirements for something to be a fighting game or a roguelike. None of the rules that say that 1-on-1 Naruto games are not fighting games have anything at all to do with fighting, and that's not even to mention Smash memes. And roguelike enthusiasts can cherrypick which qualities define the genre so much that games very much unlike Rogue can still belong to it if you use anything but the most purist interpretation, but only so long as you don't call a game that just because it uses two of Rogue's most prominent features.
If we go deeper, a lot of subgenres don't actually have very descriptive names. Just look at this thread - not everyone even knows what "hack'n'slash" means anymore. It supposedly describes DMC well because you hack things AND you slash them, but not nu-GoW, Bloodborne, or, say, Chivalry. And Diablo? That must be a point and click adventure, because hack and slash is already taken. MOBA is a ridiculous name that can mean almost anything - people even used to call Overshit that with various degrees of seriousness. But if we assume that that's true, how is Quake 3 not a multiplayer online battle arena? And how is Overwatch not an arena FPS when it's an FPS on an arena, just like Unreal Tournament? And what even is an RPG if you neither roleplay in most of them (and in case you do it's an "immersive sim", not RPG), nor do they have anything to do with tabletop RPGs that original RPGs vaguely resembled anymore?
I mostly just wanted to say the first paragraph, the rest is a slightly longer "Is this actually a problem?".
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It also seems like part of the confusion here seems to stem from people thinking that "character action" is supposed to be an entire separate genre, like racing or puzzle, rather than a subset of action games with some common features. I don't browse twatter unless it's for Japanese artists, but I'm almost certain that none of the fags that use the term mean that it's actually its own genre.