how does one relate story elements via typeface?
Ha, most difficult question! I have near-zero experience with that so I can't say much. I'd start by getting inspiration, preferably with hand-drawn type. Here are some of my typography bookmarks:
Type Theory,
Friends of Type,
Jessica Hische,
Typography Served,
Typeverything. Might be a good thing to check gaming sites too.
I can think of two ways to do it: either be literal (make some letters in the shape of feathers, barbed wire, chicken bones, forks and knives, clocks and clock hands, spacey things, you name it) or not literal (letter shapes that just aim to convey an atmosphere, don't ask me how but in the same vein as typical horror or western movie posters type).
While you're at it, maybe give more thought to the game name, too; could use a more fun, engaging twist.
And yeah, the screen does need that badass chicken =)