I want to defend the argument that video games can be works of art. Unfortunately, the term "video game" refers to a broad range of games, from classic arcade games like Pong to the latest role-playing games like Bioware's Mass Effect series. I think it's obvious that a game like Pong hardly meets the criteria of a work of art. What kinds of video games are plausible works of art? In my view, a video game that is essentially a work of narrative.
It's perhaps easiest to see how these kinds of video games can be works of art when one compares it to motion pictures. An artistic video game, like a film, is a composite form combining certain elements of the literary, visual, and performative arts. Many of the comments Rand makes about the nature of film, apply to video games as well (see Ayn Rand's essay "Art and Cognition" in The Romantic Manifesto). Rand observed that "in motion pictures or television, literature is the ruler and term-setter [...] Screen and television plays are subcategories of the drama, and in the dramatic arts 'the play is the thing.' The play is that which makes it art; the play provides the end, to which all the rest is the means." (Romantic Manifesto p71) Here, Rand observes that the "literary" element of a film, the narrative, is its essential element, the end to which everything else is only the means. The essential element of an "artistic" video game, as for film, is this narrative element. The background music, the voice acting, the animation, the actions of the player etc. are only the means to the actualization of the video game's core narrative.
What makes video games distinct from film is obviously user input and player involvement. Some see this as problematic.
Some assert that players contribute something significant to the game, that players are active forces which are able to affect and shape the video game, effectively overriding the sense of life of its creators. (This viewpoint seems to be shared by the questioner who assumes a player has "the ability to control the progression of the plot and the success of the main character.") It is true that a player makes choices—he is able to direct his little visual avatar to do either action A or B, to physically move a joystick or press either X or Y, etc. But this is no more of a "choice" than a footnote is. A player is not able to control the plot anymore than a reader who must physically turn a book's pages—you either do what's required to finish or you don't. More importantly, a player has no control over the sense of life a video game projects nor does it make a video game any less selective or stylized according to the metaphysical value judgments of its creator. A player can only do what the creator has enabled the player to do. This is true of all video games, artistic or not. For example, in many online games, massive numbers of online players can shape all aspects of the game's "virtual reality." But even then, players stay within the framework the game's creators have built. This is even more true of artistic video games that have a core narrative that a player has to actualize.
To summarize, not all video games rise to the level of art. But some, who use aspects of the literary, visual, and performative arts—aspects like background music, voice acting, animation, etc.—can be and are works of art.