Hey guys, awesome discussion you got going here!
I'd be a little carful with categories because there are a lot of things that don’t fit into nice tidy packages. Categories are a very useful tool but you have to consider their limitations and arbitrary boundaries. In the case of e-learning and serious games I would suggest thinking about it like a spectrum... Some games are made for entertainment and have educational value while others are made for education and have entertainment value. There have even been entertainment games which aren't very entertaining and educational games which could be better... Chances are you will eventually find something that doesn't fit your category system and then you might be a bit stuck.
If you want to put a definition on it then ‘a serious game is game with potential use beyond entertainment’ is a good place to start. Usually this would fall into the realm of education as games are great for transferring information and walking you through complicated tasks. However, this could also apply to other things such as games involved with citizen science like Foldit, Faxinus or Galaxy Zoo.
If we are focusing on teaching then you may also want to think about the educational objective. Are you aiming for learning or conditioning? The difference here being that learning is done through trial and error while conditioning is pretty much drilled into you through repetition. As an example, learning is great when you are trying to understand something like science but might not be the best idea for health and safety…
It may also be important to consider the learning environment. Are you researching serious games for the classroom or for general education e.g. self-learning? Time and the amount of content needed to cover is always an important consideration with classroom use
My suggestions for researching serious games would include:
Arma 3 (great for orienteering!)
Minecraft EDU (educational Minecraft mod by TeacherGaming designed for the classroom).
Kerbal EDU (educational KSP mod by TeacherGaming designed for the classroom).
Foldit (game about proteins that helps actual research).
Fraxinus (Facebook game developed to help combat the ash dieback disease).
If you’re after a military game then Arma 3 is a good choice. If I remember correctly Bohemia Interactive have also developed training software for the military.
Feel free to pop over to www.edu-gaming.com if you’d like to talk more about e-learning J