The gaming-industry is a HUGE one and though one may think there should be plenty of room to step in and participate, the truth is, it's very hard to get and maintain a job in the gaming-industry. That is, when you're looking at big companies, making big games.
Anyways,... with the enormous growth and increased popularity of the INDIE-scene, we more and more often see small groups of people find some measure of success by creating fun and unique little games.
Now, considering that it's relatively easy to just start making game on your own or a couple of friends, I'd have to say that INDIE game-development may appear to be the quickest way in. However, I'm pretty sure that's it's immensely underestimated. Most people just don't fully realize how much work it is to make a game. Most will give up, some will prevail and a few will hit a gold-mine.
So, now that I've properly talked it all down... let's get to the meat of your post, shall we;
In your post, you mention working on your degree in English Literature, but no mention of having done any other things that might be needed (such as; programming, art/drawing, 3D-modeling). Based on how general your question is and not mentioning any other specific skill, I'll just assume that you've only recently discovered that feeling/desire to get involved in making games, but have not yet figured out what to do/learn exactly?! (please correct me if I'm making incorrect assumptions)
I guess the first thing you should find out about yourself, is; Where do your passions lie? Considering that you're a man of Literature, I'll just boldly assume that you're very much into "stories", whether it be books, movies or games?! You've probably also already done some writing in the past (short-stories?) or you're actively blogging about something... and here I'll assume it's often about games, or you're looking for ways to combine writing with a second passion/hobby, gaming.
I'm pretty sure that a lot of game-journalists started out just like that. Just try writing a few reviews, or short-stories about your experiences with a game, or even take some of your favorite franchises and write short-story spin-offs. Sure, it's difficult to get noticed on the web, but if you let your work shine with a unique point-of-view, presentation or humor (or any combination) and focus mostly on your writing first, sooner or later you will grow a following. Just don't try to push your work into everybody's spam-folders, just to get the word out. Building a skill and gaining experience is of more value to you....
...So in conclusion; If this last bit seems like it could be a comfortable angle to approach writing, while combining with gaming... you may eventually find yourself with more and more story-ideas in your head you could jot down, until you have enough to work with and you start to write a book or a possible script for a game-story.... and I guess there are still plenty of other approaches to accomplish something similar to this.
Never forget, you'll probably still have to find your way through experimentation/research/study for a while, before your career path becomes clear. You will stumble and fall, but so long you keep moving towards that horizon, eventually you will see where you're going.
Lastly, also don't be afraid to step out of your comfort-zone. Try something new, learn another skill (art/design or programming) or consider other industries to write for (theater, screenplay-writer, novelist, dialog-writer, movie?)). You may just find, that your second passion/hobby will just be exactly that. A hobby.
And yet, you may also find, that while researching things, you discover new interests, other than writing. Maybe you find that drawing and art or concept-art is right up your allay. Maybe you find that programming is pretty cool too, or you learn to be a good animator.
Who know?! ... who knows what the future holds!?
NOTE: If my assumptions were way off, and you have programming experience and other skills to get into development, try to read between the lines. There are a number of subtle, but important points I'm trying to make that still apply in such case as well.
PS: I had my reasons for this long-winded post, so just ignore the fact that I didn't give a short answer. It was on purpose!