Just about every social situation imaginable. I've gone through huge amounts of anxiety here on the Escapist, despite it being, well, non-threatening.
I'm bi-polar and from what I've discussed with my councilor is that it's possible that made me neurotic. The idea for this came to me from an old Mac Hall comic that I've imbedded below.
See, your mood can be considered a "reward" or a "punishment." The mania could be considered a reward, the depression a punishment. But neither of them come based upon any real form of outside stimulation. It's all random firings that are triggered for reasons that are completely beyond my knowledge. I can't recognize a pattern within my insanity, but that doesn't stop my mind from equating interacting with other human beings as the worst form of pain.
I can't handle being in large groups of people. These people don't even have to physically be near me, either. Back when I still played WoW, I could never get into raids, because the mere thought of doing something like that would send me into a near panic attack(and, sometimes, full fledged panic attacks). I could barely manage to get into 5 man groups without falling apart, though I somehow managed that.
It didn't even matter that I was in an entirely friendly environment. If I messed up, no one was going to yell at me, because they all knew I spent a lot of time trying to be as good a tank as I possibly could. The guild leader was my best friend that I knew growing up. Even if someone did try to do...whatever mean thing you can actually do to someone in WoW, he'd almost certainly back me up. With him would come the backing of the rest of the guild undoubtedly.
My suggestion for your game? Avoid bright flashing lights and sudden sounds. Imagine you're trying to tame an animal. Speak low and softly, no quick movements, and you should be fine.
Edit:
Repetition should also be considered as well. Anxiety(really, all forms of fear) are an extension of ignorance. You don't know what's going to happen; what X is going to do. Knowing what's going to happen next, what's going to be coming down the pipe, what you're looking for, will all do wonders for creating a relaxing environment. Might not make for an engaging or fun experience, though.
