I think the more productive way of thinking about it has to do with why one engages with art. Does it give you a way to socialize through discussing critiques? Is it a tool for inciting empathy? Do you simply want to bask in the emotions it inspires? And so forth.
When you look at it from a perspective of what you want it to do for you, then I think you can make a good case that for some purposes, games would work just as well if not better compared to books, movies, sculptures, dances, etc. Whether or not you call it art... isn't so important, really.
Perhaps also To The Moon, by Freebird Games.
A better way of seeing why games can be art is through a comparison to movies. Games can be made to essentially be movies but with the crucial difference of immersing the viewer entirely into the world through the choices it presents.
I do not see how adding more possibilities to an existing art form (movies) can ever demote something from art to non art (whatever you think these things mean).
I think a game like last of us is a great exploration of the potential of this form of game play.