If you're going to try to whip up something over the holiday break, see what you can do with the characters and storylines of that company's top game(s).

Videogame scripts aren't like screenplays exactly. In a screenplay, the actor can read the whole thing and figure out what his/her character's role is. But videogame scripts are often missing a lot of information that would inform an actor. Don't try to write the script for an entire game - just a couple of scenes that could show the depth of your writing.

To answer a question with more questions: the company is local, so where do you live? What degree do you have? What games have you worked on? Have you had any of your writing published, or used in media?

So you're applying at a triple-A company. Tall order! Your published stories definitely belong in the portfolio. Do try some dialogue for some of that studio's past games (especially the ones they'd likely continue with). https://reflections.ubisoft.com/games/ shows a wide variety of IPs. Try some dialogue for Tom Clancy, Far Cry, Watch Dogs...  Go get your hands on as many games as you can from that page. Read a real Tom Clancy novel or two. Understand what makes the characters tick, and how they talk (in those games, they're American tough guys mostly, but what life experiences made them that way?). Master American idiom (Americans say "elevator" instead of "lift," and "intersection" instead of "junction" or whatever Brits say - you can find info online). 

And no, I don't know offhand where you might find some scripts. You can try Googling, but don't count on finding much. You can also ask in the Writing forum.