It's a new form of art, I'd say. It's not a passive experience like movies, but rather an active form of immersion, which is different but equal, in my opinion. You really should get her to define her version of 'art', because it seems to be a major factor in these things.
If you go by the whole fractal Science - Art - Philosophy method, of course it's art. Everything is part art, part science, and part philosophy, so games can't be signalled out for exclusion.
If it's the whole 'art evokes emotion' use, then of course video games count. How often do you play a game and feel nothing at all, and just consider yourself moving pixels on a screen?
Art conveying a message would be the same as the above.
It seems like her dismissing it all in one swoop without considering it first. It's not a wise way to treat anything, at all, but she's a teacher and they're trained to parrot what they're told to teach (no offence to teachers of course, not all actually follow that in practice). Chalk it up to arrogance, or try and intelligently debate it with her. If she doesn't listen or shuts you down, it's arrogance. If not, then it's ignorance.
If all else fails, do what I did: humour the teacher and try manipulating her as a personal game. Heh...now I sound evil...
EDIT: Oh, and on the 'worthless technology' stuff...try telling that to the war veterans and psychologically scarred people that use them to overcome intense issues that are otherwise nearly incurable. Seriously, tell her to research psychology of play and the studies of how virtual reality technology is being used. I'm not saying video games are great for your health, but in some circumstances they can be.