I'm pretty sure most multiplayer PvP games are created to invoke rage.

Competition. Exactly. Its a game. 

I was just joking around.

Art is such a broad term that it could define literally anything, from paintings to porn.

Here we go.

Video games are interactive. That's really the only technical difference between them and traditional forms of art. People consider paintings, sculptures, books, plays, etc. as viewed by the observer, while with a video game the observer is actively generating the experience. I'd argue that the role of a "player" in a video game is just as important in other forms of art. This is just a bunch of paint on a very old wall.

An observer is necessary to turn it into something greater. I'm lucky enough to have personally seen this work, and the experience upon entering the room was amazing. Words cannot due it justice. It just spoke to me, and my feelings and emotions spoke back. In a metaphysical sense of the word, I'd definitely describe it as an interactive experience. I wasn't just veiwing the art, I was a part of it.

All art needs an observer, a "player." A great symphony is just random sounds until it's heard and mixed with that individuals thoughts. We see art that we can appreciate for what it is, but there are other pieces of art that just speak to us. One example for me was the winged victory.

A tldr: version of this would be when you're looking at tons of magnificent artworks over and over, but on one specifically you say to yourself "oh I like this one." The observer is an integral part of making it art verses just an object.

Now that I've argued traditional art is like a game in the fact that it's interactive, I'll move on to just focusing on games that are art. First up is one I made myself. I had lots of experience making parts, sections, and aspects of games but this was my first game I made start to finish. It's unpublished and I didn't have the legal rights for many things so I can't share images of it, but basically there was no gameplay. It was a very abstract experience involving the player just walking forward. My goal as a creator was to delve into what it's like to go insane. This wasn't happening to the in-game character though. It was happening to the actual person playing it. Yeah it was kinda like brainwashing I guess. If that's not art I don't know what is.

Moving on, there are a lot of other examples of games that are certainly art, even if they aren't the best art.

Journey:

The Unfinished Swan:

Protious:

The Last Of Us:

Super Mario 3D World:

Ico:

Limbo:

Tearaway:

Now I know the person who disagrees withme right now is going to say parts of the games are art, but the game itself isn't. That'd just be a silly thing to say though. Is a movie not art because it's just a filmed play?

Is this not art while the pictures are? In many cases the collection and arrangement of art is art itself. Games certainly are no exception.

My last point addresses the fact that the games industry makes a boatload of money. It's true. AAA games cost millions upon millions of dollars. They are a business. Art has always been one too. Michelangelo didn't work for free you know. He charged about $420,000* in today's terms for the Sistine Chapel's ceiling. Is that fact all of a sudden going to turn his painting into a corporate production instead of a piece of art? Of course not. The financial origins of any piece of art can't be held against it.

My final conclusion is that video games are certainly a valid artistic medium. The art teacher in the OP is probably just lacking of experience with them.

*http://www.quora.com/Fine-Art/How-much-money-did-Renaissance-artist-Michelangelo-make-What-kind-of-lifestyle-could-he-afford

Every games is art, i guess your GF too rigid about art definition. How a game is not an art ? it got music, graphics, etc.