You have a few very specific goals.
It's one thing to be a super fan boy, and dream of writing for your favorite franchise/ game, It's another to just get in the door to be a writer.
Is your major English, journalism or something like that?
The thing is, writing is a tough gig to get, everyone who can type thinks they can be a writer. Often or not, it usually comes down to who has formal writing background/ experience. Writers often excel in English composition classes, and usually have their own private portfolios of work.
If you don't have that, I'd look into getting some words down somewhere. Although I personally don't blog, it can be a way of getting yourself out there. Blogging is not really serious writing tho.
Most writing jobs will require familiarity with script writing. (For creative writing).
If however, you want to write reviews and news articles, look at some of your favorite outlets, and see the style they have.
Technical writing is also where a lot of the jobs are at now a days, that;s not really sexy work, but it can establish your cred as a serious writer.
Are you good at research?
Writing and research often go hand in hand, it's expected that if you write something, you have the data to back it up.
The other thing to consider is that writing is an often denigrated role in the game industry. I personally think it's because it;s such a masterful role in all other industries, where writing is king.
Also, It's important to note, that writing for games usually is writing all that is necessary for the game, like menu options, descriptions, it's not all boundless lore.
Unless you get in at the ground floor of a project, you also won't likely be the one who is writing the overviews and the major plot points. All that core work is done by the lead writer often then not. In other words, you often don't get to choose what your writing about.
Not to mention, there is a whole style and form for writing interactive narratives, vs. the standard game narrative/ lore.
I'd start asking yourself more questions as to what kind of writing you want to do, rather than just where you'd like to do it.