So I got Dragon's Dogma because it had very, very good reviews and every single opinion out there I've read said it was great.
Played for a bunch of hours, and I could see it. Yeah, the combat is very nice, the monsters have cool designs and so on. But the story was non-existant. You get your own personal slave through a magic portal while you're just walking around and people are like "Oh yeah, they do that. Now he is your slave. Good luck." and I'm like "This **has** to have some good explanation behind it, right?". Well no, not at all. It's just a gameplay device. I got completely put off from the game. And I can't really understand how it has so many positive reviews.
Now, you read that you'd think all I play is adventure games or visual novels (actual visual novels, not the lightly disguised porn), and I actually do not. I'm not a fan of adventure games, and text based/visual novel kinda games bore me a lot.
But what about graphics? Well I'm still #*@!ing pissed that Bethesda can't #*@!ing pay a good engine team. They make cool RPGs that look dated on release date for some damn reason. It's like "Oh you know all this good work that our employees did? Well lets show that in the most barely passable way we can put out." Like if you valued your dev team at least a little you'd make sure the shit they put out looks the best (and as fast) it can, but they don't. So their games are clunky, visually dated, and unoptimized.
On the other hand, you see craftmanship in the art. You can see the artists are trying to squeeze the most value out of their 1k textures, in one way or the other. And that makes you appreciate things more. You might never get proper shadow mapping out of their games, but you see consistency in there.
What I am trying to say is that what puts me off is laziness. You can see when something was made passable on purpose and you can see when something was made as good as the dev team could make it. And the later is the kind of thing that makes you stop on a game, and think "Hey this is pretty cool". It is the combination of "Hey these shooting mechanics feel nice, the environment is interesting, and the music is just right" and so on.
As an example I picked up CrossCode a while ago and it's pretty damn impressive. You can see that the sprites are made with care, the characters are made with care, and the environments are made with care. You can see in the game that the developers gave a shit, and that is, in my opinion, pretty cool.
I do have in mind that there are games that exceptionally pull through despite lacking a lot in some of the "pillars" you mention. Say, Vampire Bloodlines combat is absolute shit, graphics were okayish even at release date, but damn dude, the world just grabs you by the balls and keeps you there until you finish the damn buggy mess it is.
So in the end I find hard to say what makes a good game. I've played and enjoyed visually bad games, I've played and enjoyed games with frustrating gameplay, and I've played and enjoyed games where the story is serviceable at best.