Whether or not graphics are important is, I think, mostly a matter of opinion. Graphics have never really mattered that much to me. I’ve played games with nothing but text as graphics and still had fun. I’ve also played games with good, modern graphics and had fun. However I think that good graphics can and usually do add to a gaming experience. I’m not strictly talking about photorealistic graphics. These matter, and are important, but I’m really talking about graphics that suit the game.
Each game has its own style and atmosphere that it aims to impress upon the player. Fitting graphics are important. Whether that means blocky, pixelated graphics, almost no graphics, cartoony graphics, or photorealistic graphics, depends on the game, and what atmosphere the developers intend to communicate. I believe this is also true from a business perspective. You might want to design the graphics around the preferences of your target audience. (Of course, there are plenty of exceptions to this, and I’m no expert, but it’s a general observation.)
Are they going for a retro nostalgic feel? Perhaps those blocky graphics would be a good choice. How about the latest Halo game? Realistic graphics are probably fitting. Making a text-based game? Why bother with too much in the way of graphics at all? Perhaps you want an artsy, unique feel to go with your equally artsy, unique game? This could be any graphics style, really.
As I said before, I feel it’s mostly a matter of opinion. My opinion is that if the graphics add to the experience, then they’re ‘good’ in my book. This includes what some people may consider ‘ugly’ graphics. But what I really look forward to in most games is gameplay and storyline/character development. Graphics are important, but not nearly as important to me as these, and for me, graphics do not always need to be at a level of ultra-realism.