The cynic in me suspects that data science for a game company will involve mostly marketing research, however.
Actually, there's a lot of it involved in game design. In the case of MMORPG, what to develop next as extensions or monthly content packs. In the case of single player games, feedback on building sequels. A lot of game developers these days put effort into gathering all sorts of telemetry from their games, RPG developer Bioware for example knows how many hours the average player spent on Mass Effect games, how many finished the game, how many made a customized character vs how many used the default face, how many played a female character versus male, how many imported saves from the previous games, which quests were completed and which were skipped, how much of the dialogue was skipped and many other things that are used to understand what to focus on for their next games. And it's all on a solo RPG, so they had to deliberately add some online analytics reporting functionality and are not just using stats that was lying around on an online game server log.
Guild Wars 2's developer arenanet is employing a data scientist and economist, John Smith, to manage and keep control of the virtual economy in their MMORPG. He's also head of the analytics team which is the primary decision maker on what content is going to be cut and which is going to be developed in the future.
Marketing can be a part of it but more and more, analytics is getting to contribute in game development decisions.
One the one hand, it's cool that they are forward thinking about using telemetry to improve their products. On the other, it's a little upsetting and disheartening that I played plenty of Mass Effect and don't recall ever being given the option to opt out of telemetry. And I am the kind of nerd who will scroll through all the game settings before I even start.
That's what I did in a game company, I for example plotted (time or matches) vs. experience + # of people who made it that far for all players and identified a choke point where a large part of players had a long interval with a little progress (and so they dropped off).
Designers need help, some of them are fluent with (big) data but most aren't - and you can be their partner :).
Check out job openings at Blizzard, Riot, EA, Ubisoft, etc. Or pick a game you like and reach out to them through your extended peer network. If you live in (or know someone in) the Bay Area you are less than the proverbial 6 degrees of separation from someone who works in games.
Caveat: Unless it's an established studio turning out a reliable set of moneymakers, the job is going to be very unstable. It's like a combination of movies + startups. You will work your ass off and if the game is not a hit the company will fold and you'll be on to your next gig, if you can find one.