Depends on how you define "art." I think of art in two ways - art with a low-case "a" and Art with a capital A.
The former is any type of creative expression. Doodling by a monkey can be considered art in this sense. There's a continuum. You have bad art (monkey doodles) and good art (a beautiful painting or graphic design). All videogames are art in this sense, just by definition - they are a product of creative expression. That's how most people think of "art" - anything from their daughter's doodles to a painting - so from that perspective, yes, videogames are art, because they are a creative expression.
Capital "A" Art is a different animal. That's also known as "high art" - what would be called Leeteratuuure in the world of novels, as opposed to commercial fiction. The classics, for instance. Likewise, in film, there is the distinction between artistic masterpieces and regular movies. Regular books or movies don't try to do anything much besides entertain and move you. "Art" in the capital-A sense does more - not only is it beautifully constructed but it also expands your mind and soul; it elevates your perception and experience of life. In this sense, videogames are not Art. They are entertainment. And that's usually how I think of them.