I guess it depends on how you look at it whether or not your own definitions of genres are fitting...
I find that Dark Souls is an RPG, since while the "Story" is themed on loneliness, survivability and the inevitable end (Based off what other NPC's you can meet talk about, they mostly mention about trying to not turn hollow by "Dying" too much and also mention how glad they are to actually see another non-hollow person)
The gameplay, is very action orientated, there's no puzzles, not really a huge amount of exploration (Most areas are fairly linear, with a few side paths and shortcuts and some "Hidden" items) the focus is mostly about the combat.
But there's also the RPG elements, stats which you CHOOSE to level (Not only do you choose whether to spend souls on leveling, you choose what stats you level giving character customization), there's many different weapons and armour all requiring different stats, different ways to upgrade weapons changing how stats effect them as well as their performance, there's a multitude of spells of 3 different catagories (Miracles, Sorceries and Pyromancies) requiring different stats and allowing customization of which ones you will use (Since you only have limited spell slots)
This comes off as a "Action RPG" with some horror themes (Not Horror in the sense that "Horror" games these days often are, which rely on jump scares and gore to try and cause fear, Dark Souls is horror in the sense that it creates tension since death has a fairly hefty cost (Being sent back to the last Bonfire you used and dropping all souls and humanity) this can also be combined with the shock of seeing some of the monstrosities you have to face for the first time (E.g. The Gaping Dragon looks intimidating as fuck, though later you realise it's a pushover))
Blanket terms are really not that great in my opinion (Not just for games, certain films and a lot of music also are not satisfied by the blanket terms/genres that they tend to get) but I get why they are necessary, in order to try and tell people who have no information about it what it's like.