To some extent, graphics are important because with extremely primitive graphics, like the graphics of the NES, it can get difficult to tell what things are represented by the image, and the limited color palette presents a challenge in making the game look aesthetically pleasing.
A game doesn't need the most advanced graphics to look aesthetically pleasing, though. It can be made up for by using an art style that doesn't need powerful hardware, e.g. modern pixel art, or the simplistic, cartoonish look that 3D Nintendo games use. Mirror's Edge still looks great due to its art direction and use of techniques like precomputed lighting.
However, different people have different standards. I've been really enjoying playing the game Crypt of the Necrodancer, and I think the pixel art is also pretty good and aesthetically pleasing, but when I showed the game to my friend to see if he might like it, he rejected it because "the art didn't speak to him." Evidently, compared to me, he has a higher minimum for graphics in order for a game to be fun for him.
A game doesn't need the most advanced graphics to look aesthetically pleasing, though. It can be made up for by using an art style that doesn't need powerful hardware, e.g. modern pixel art, or the simplistic, cartoonish look that 3D Nintendo games use. Mirror's Edge still looks great due to its art direction and use of techniques like precomputed lighting.
However, different people have different standards. I've been really enjoying playing the game Crypt of the Necrodancer, and I think the pixel art is also pretty good and aesthetically pleasing, but when I showed the game to my friend to see if he might like it, he rejected it because "the art didn't speak to him." Evidently, compared to me, he has a higher minimum for graphics in order for a game to be fun for him.