What other story can the OP have told than his own? It is a role playing game and it does not have a fixed plot.
If it's in your own words, then most teachers do not consider it plagiarism, however, if it's C&P'd then I would worry...
As a former high school teacher, I think it depends on what was the original assignment. Both of the above opinions which are represented in this thread (I just chose the most recent two while I'm writing this) could be correct.
Was the assignment to create an original story line or something similar? Then, there's a case for plagarism, or at the very least, not completing the assignment properly. There is a clear storyline in Skyrim about a hero escaping death and dragons, becoming a "hero" for lack of a better term, and then helping the local citizenry. How the player goes about it in game doesn't matter. That's the story line for the beginning parts of the MQ in the game. If the OP just writes a story about how his Wood Elf archer (or whatever) went about this whole thing, then maybe it's ok.
But counter to the point - what if he told the story about how his father and brother were killed by the Thalmor, then he was raised by his uncle and travelled the world, then returned to Skyrim and lead a fight for Freedom. Stormcloaks? Or Braveheart? Plagarism? I don't know, depends on how closely it follows the storyline. But a clear case of inspired storytelling. But NOT if the object was to come up with an original story. OP didn't do that.
So, I've digressed, but I think plagarism would be hard to prove BUT there's a case for it depending on the assignment. Also, OP, I think you're risking a considerable amount of what I'll call "teacher goodwill" by letting her believe you came up with this great storyline that she's now going to share with others. All you'd need to do would be to say, "Hey, teach, by the way, I based it on a video game I play." As opposed to thinking you've got one up on the world, you ought to just open the dialogue, let her know where it came from, and then go from there.