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If you ask me, a game has to be tied or close when it comes to fun, story (if applicable), and music (if applicable) in order for me to even care about a game.
You could throw a text based terminal game using ASCII art at me and I'd love it just as much as a game such as Hitman Blood Money so long as it's fun enough.
Indeed.
Graphics will always be less important
The popularity of various "ugly" games is proof of that
undertale
Rimworld
Dwarf fortress
Minecraft
Diablo 2 (not resurrected)
Probably many many more
You'd think that everyone thinks that way, but the overwhelming majority of my "normie" friends won't touch a game if it doesn't have good photorealistic graphics and animations.
My dad is one of those people who seems to think minecraft is lame because of the graphics yet says Mario on the NES looks just fine.
Minecraft is a strange one for me, because it has never caused me that reaction of "this game looks bad/ugly". I think something like Infiniminer looks ugly, Unturned looks ugly, most Minecraft clones look ugly, a lot of more "realistic" games look ugly, but somehow not Minecraft. I can't quite put my finger on why I see it as different somehow.