Best article Ive read on the subject
http://clicknothing.typepad.com/click_nothing/2007/08/on-authorship-i.html
If it doesn't convince her, it will completely go over her head, confusing her and makjing her look like a fool.
For another summery, go here and skip to the post, "What Is Art?"
http://gamedesignconcepts.wordpress.com/2009/07/
If you can bring actual games into it, check out the example games in that last link, particularly The Marriage and Passage. If you can branch out a bit into games you have to pay for, check out The Path and The Void.
Expand your argument by going into analog games. One that comes to mind is a theater show I read about that involved audience participation. The actors acted out their parts, and the audience was allowed to interact with the actors in the plays context. This could change the outcome. This is definitely theater art, but more importantly, it is also most certainly a game.
Remember that the term, "Art" is a pretty nebulous concept. Ask her to define it, and she will likely be stumped, put forth definitions that arn't terribly useful, or try to alter her definition to fit her hypothesis that games are not art. For that matter, have a definition for, "Game". This is even more confusing then "Art". The best one Ive found is "A series of meaningful choices". Have your own definition, like from that second link, and explain how Games fit. One point you will have to concede is that most modern day games don't fit the lofty ideal of what I call, "High Art", because they are simple power fantasies. At this point, you can point out the number of action movies that are far more noticeable then your "art films", and even how most Norse mythology is basically a murderous psychopaths wet dream. Games are still a young medium, particularly video games. There is no way that we could have gone from cave paintings to the Mona Lisa in 25 years.
