I don't think anyone will dispute that great graphics help make a good game even better. However, to claim that graphics is what makes the game, well, that just sounds stupid. One can make a game of nothing but putting a ball in a cup and give it the most amazingly spectacular graphics in the Universe, and it will still be a dull, insipid, uninspired, and just down-right boring game to most people. Gameplay and game-mechanics are the two defining elements of a game as those are the things that determine the entire nature and design of the game. To use a car analogy (dear, god, I can't believe I'm doing this!), gameplay and game-mechanics are like the frame, body, and interior of the car (interior including the steering-wheel, the dash-board, the peddles, the gear-shift, the seats, all the controls and how those controls are laid out, etc.). The graphics are then the paint, the trim, the headlights, the spoilers, the sound-system, and the clear-coat finish. (The game engine and hardware would be like the engine, wheels, tires, and suspension.) Having a great paint job and exterior trim certainly adds a lot to the excitement of owning and driving the car, but it does not define how the car operates. If it did, then chances are good the car would end up poorly designed and poorly performing in the areas where it counts in terms of overall performance, response, and handling.
Also, there is the matter of art direction. Any trained monkey can make a highly detailed, pretty picture by just following exact technique, but only a truly talented artist can make something inspirational and breath-taking, that is, art. Great art direction can make up for not having a super high resolution or massive polygon count. In fact, games with great art direction can often look far superior with low-fidelity graphics than comparable games with much higher-fidelity graphics and little to no art direction. We've seen many such examples where the developers try to "calculate" their way to artistry by trying to raise the texture resolution, image resolution, and polygon count, but even doing these things, their game still just looks bland and uninspired with almost no emotional content, whatsoever, to connect to the gamer. It's not how much detail and fidelity one puts into the imagery that creates the sense of awe and immersion; it's how the different art assets are composited together and how they are balanced with one another to evoke mood and wonder. It's in the choice of style that evokes particular emotions at particular moments. Further, you want to choose these things so they match well with the design and flow of the game, i.e. the gameplay and the game-mechanics. You can't simply calculate your way to this level of craftsmanship in game construction; you have to have some actual artistic understanding and mastery. Again, back to the car analogy, you can make your car have a rainbow of colors and a ton of trim options hanging all over the place, ending up with a gaudy mess, or your can make more artistic choices, which sometimes results in a more minimalist exterior, that focus on exactly the message you want to send about your car's performance and how it gets used (that is, the exterior is made to fit the design and construction of the car, not the other way around).
Seems lately we've been having a rash of developers coming out of the woodwork making these silly, universal claims about what makes a video game. I've noticed that many such developers are associated with triple-A games. There's a disturbing apparent preponderance of such narrow-minded, shallow, overly restrictive, and just plain wrong attitudes and thinking toward the construction of video games. It's no wonder there are so many triple-A games with boring, unimaginative, and inbred design with clunky, broken construction.