From a wonderful email asking to define serious games, comes this answer:
To the layperson, a game is a game is a game. However to those of us in educational technology (and those of us passionate about games in education) the difference between Math Rabbit and Spore are gargantuan. To define those both as "games" is akin to calling Shakespeare and William McGonagall  "writers".
An educational game (computer): aka: edutainment, is a deliberately structured and scaffolded learning activity, usually constructed with colorful, fun puzzles interspersed with learning activities. These games often require a set number of solved problems which are followed by a short animation, cutscene, or puzzle game. Learning activities are often framed within the game theme. For example, learners may be playing a bowling game where simple math problems are superimposed on each of the pins. As the player correctly answers the math problems, the pins are knocked down. When the player has knocked all the pins down, they may have an opportunity to virtually roll a bowling ball down the lane, and hit some pins, without needing to answer any math problems.
A serious game (computer): players controls a limited number of variables to effect an outcome in a specific scenario. They are usually web-based, they usually have a very specific theme (peace in the mideast, health care, politics), they are not meant to be in-depth simulations, they are meant to model the most important dynamics in a specific scenario, they are short-term games, they are deliberately designed to teach, explain an issue, or clarify the dynamics of an issue, and the point is to simplify complex issues to players gain an understanding of this issue.
Although you didn't ask, there is one other category of games - I will give a very short definition:
COTS - commercial off the shelf games, where there is no pretense of education. These games are built solely for the purpose of entertainment. COTS games can cost tens of millions of dollars to produce  but hit titles can bring hundreds of millions of dollars . When used in the context of good instructional design, COTS games can be powerful learning tools.
These definitions are mine. I give them to freely to use, but please attribute 😊 Please share your paper with me when you publish it!