Cognitive theory tries to define how we think. This is highly relevant for video games. Sadly not many academics has examined video games in this view yet, and it seems that most of the research being conducted in the field right now, is about porting existing film/philosophy cognitive theory to games. I think its a start, but cognitive theory for games needs to stand on its own.
I think it is essential to study games as a media type of their own, not just as an extension to film or theater. I strongly believe that games have qualities that make them truly unique, and as such, i view games as systems with an experience potential inside.
Emotion theory is a part of cognitive theory. Trying to define how and why people feel, as well as what emotions are. I beleive that emotion theory research in game design would be able to provide designers with crucial knowledge on how to make their game systems provoke emotional responses in players.