graphics = video
gameplay = game
graphics + gameplay = video game
Yes, from an objective view, they are important to video games. I don't think they're the number one priority, but it's pretty high up there. The situation doesn't have to be about one thing or the other and more advanced graphics generally signal more advanced engine capabilities, hence more advanced gameplay, anyway. They're separate things, of course, but where's there's good graphics, the potential for better gameplay is greater.
Thank you! Couldn't have said it better! I can't believe all the people that say "I don't care at all about graphics", or "geez, just use your imagination". If you want to use your imagination so much, why even play a game that someone ELSE designed? Why not just pretend to play out the whole thing in your head? The video part plays a pretty big role in video games, and that is where the graphics come in. When I am exploring a game's environment, I am much more immersed and pulled in when I the surroundings are beautiful and feel real. It is easier for me to identify with a character when they have a realistic face and show emotion, as opposed to the character being a white block with scrolling text. Same thing goes for sound.
Although graphics do take a back seat to gameplay, to say they don't matter at all is ridiculous. I am currently playing through Two Worlds 2, and that game is a train wreck. I will probably force myself to play through it, but damn if it isn't ugly with some terrible sound. The gameplay itself isn't terrible, but the visuals and sound and so bad that it is ruining the experience for me. It just makes me look forward to Skyrim that much more....