Games Studies is establishing itself; those interested in studying games could well try to apply their field of studies to computer games.
Basically that's how computer games studies is coming together now: Students and lecturers from various fields approaching this new topic, each from a different viewpoint.
Psychologists unfortunately tend to look at everything with a behaviorist perspective - "Hmm, a new behavior. Is it addictive? Does it make people violent? Do they stop if we lobotomize them?" ...
What goes on in the mind when we look at a @ and know it's a hero (1) is being studied more by philosophy departments, which IMO includes literature.
There, we have
narratologists (looking at how stories in general are structured, how storytelling works etc),
semioticians/semiologists (interested in how we read signs - e.g. the word "dog" is neither furry nor does it look like an animal, but it makes you thing of one: How?)
ludologists (interested in how to categorize and analyze the ways in which people play, or use playful behavior. They seem to have an unfortunate tendency to generalize rules for analyzing games in "all cultures, all times".)
cultural studies would be more interested in the roles which games and playing games has in different cultures. Can gaming be subversive? If not, why is China so strict on gamers? What about the early internet's hacker ethos and cyberpunk literature? That, and probably ritual games in ancient greece as compared sports now etc.)
On a more practical approach, there were books great for teaching, though I'm not sure if it has its own name as a field of study: Turning away from the classical method of describing "how and why the (work of art) is beautiful" ("literary aesthetics) or how it relates to the culture it was made in ( authors such as Bordwell/Thompson, Graeme Turner studied the relationship between the financing of (film) projects, the audience and the process of selling the (film) to the audience (using postmarxist theories to some extent). Applying that to games would look at how, for example, the various game age ratings systems such as PEGI and FSK influence a) the way games are made - companies sometimes make different versions of a game, one with green blood and robot parts, another with red blood and gore chunks; b) influence the content of big-budget games (since the intended age bracket is set early in development. Age 12+? Forget about sex, swearing, alcohol, tobacco, drugs, and violence ...)
On even more practical levels, if you're into economics, programming, etc, there's be lots more potentially interesting research but I can't tell you much about it >
If you're looking for more info on the academic debate on games, here's a few links -
Digital Games Research Association http://www.digra.org/
One of the better-known ludologists, currently at MIT http://www.jesperjuul.net/
Wikipedia http://en.wikipedia.org/wiki/Game_studies
Good introduction to the academic debate, in German though: http://www.playability.de/pub/drafts/Invaded_Spaces.pdf
Game Developer Magazine online - some (not very academic) gameplay theories by designers, lots of interesting post-mortem and technical stuff about making games. http://www.gamasutra.com/
Toady interview on Gamasutra http://www.gamasutra.com/view/feature/3549/interview_the_making_of_dwarf_.php
(1) [I think I gave a fellow WoW player a bit of a shock recently when I started up Angband (another roguelike) and said "Look, my new level 35 rogue ... got an artifact armor ... ". If you can explain why he was shocked when I pointed at my roguelike hero @, and what the difference between the @ and the WoW char is, you should study semiotics :-]