In Gamasutra, Tom Heaton’s come up with a framework for the cycle of interaction between the player and the system. He talks about the player (I keep writing ‘learner’ :) perceiving the system’s response, analyzing the situation, and implementing an action which is then executed, and the game engine calculates a response. He carries it forward as a tool to analyze a game, where if the play experience isn’t sufficient you can use the framework as an way to look for problems.
The problem is, of course, that Don Norman’s ‘Gulfs of Execution and Evaluation’ model does it far better in my opinion (it’s in his Design of Everyday Things book, which is highly recommended). It’s designed to understand the usability of a system so is very cognitively-oriented, and it may not capture the emotional side without some work, but overall it’s richer and consequently more practically useful.