Atmosphere alone can do a lot, like Limbo..not really so much of a story or graphics, the gameplay is typical 2D affair but it definitely had enough atmosphere to engage your curiosity and make you want to finish it. I like the feeling of creepy and mysterious that it gave me and the ending reminds me of the feeling I used to get from watching Twilight Zone as a kid, filling my imagination wondering wtf?
But again, genre...Other types of games like FPS don't typically have much atmosphere without graphics to create it, like Metro, the lighting, fog/smoke..etc are what gives it that atmosphere. So again it really depends.
I still play NES games and still enjoy the music too. But a game only needs that 1 thing to make it fun for you to play and that will vary depending on the individual.
Some games like Project Cars only have good sound effects, physics and graphics, but it's realism of driving a race car is what makes it fun to play.
If you literally never, ever buy or enjoy games unless it meets all those criteria that you mentioned, then I'd say you are quite a unique gamer.