All elephants are grey; not all grey things are elephants.
Likewise, games can be artistic, but not all games are art. Portal and Portal 2 can be heralded as unparalleled in art, gaming, story, device, etc., and can be argued as such, but few would argue that Duke Nukem Forever or Call of Duty will be anything more than a game. Hopscotch was a game, but it is far from art. Something like Bastion, however, with it's tasteful blend of imagery, audio, gameplay, story, and character, could be considered art and could simultaneously be considered a game. Minecraft is a game, as much as playing with Lego is; art can come from the creations, but the product itself is not art--it is why paint is not art, nor is canvas, but paint on canvas might be art.
But, to his other point, of saying that art is something that makes us reflect on ourselves, then that is a subjective matter. I have reflected on myself in Assassin's Creed, while killing a guard, and suddenly imagining his family learning that his easy job strolling a rooftop, to pay the rent, got him killed by an unthinking assassin who could have done it much better by sneaking around. It got me to the point that, for a time, I completed a mission or two with only the minimalist of kills, or none at all. I have tried driving as carefully as possible in sandbox games, knowing that insurance is a *****, and I would hate to be that guy who gets some asshole that plows headlong into the side of my car, reverses, then drives off again, with no cares about me. Things like this have made me reconsider myself, and put my life in view.
But then, I get past it, knowing that this is a game, much as I know that the characters in a book that die can be alive again if only I start reading the book anew.