Yeah, there's a time to stand up for what you believe in, but there's also a time to know when you should've known better. As you said yourself, it is a semantic argument. Anything you can say about her, quibbling over details, could inversely be said about you. I too happen to believe in the games as art argument, however it's no secret that this isn't the societal consensus. I would ask her as politely as you can if she might allow you to make your case, either after class, or even in a scheduled teacher-student meeting type thing. If she's unwilling, then going another level up in order to appeal her unwillingness to hear your case might prove fruitful, but if the administration feels the same way that she does, you might find yourself living Sisyphus' life story.
Alternatively, one option might be to try to take the case to your student council. Now, student councils are generally useless party planning committees, however if you can convince them to appeal to administration for you, you might have a better chance getting them to listen to you. They're a little more likely to be open to at least holding a debate about whether or not games are art, and if they'll consider it at least a worthy point to argue over, you might be able to make the case that from the perspective of your own generation the debate about whether or not games can be art is a legitimate topic, and because of a semantic misunderstanding created by a generational gap you decided to write about what you felt was art, and thusly were working within the context of the assignment, because the ambiguity of the word "art" had not been consensually agreed upon between you or your teacher.
On the other hand, they might point out that you should've asked her if she was alright with that interpretation of her essay to start with. If she pulls the "you should have asked first, and I might've considered it then" card, you might be trying to save a sinking ship with a spoon.
