I'll propose that type III fun is when you're having fun while you're doing it but afterward you're absolutely miserable as a result, such as after a night of hard drinking, or a weekend of nonstop sleepless gaming.
My brother always says "It's either good, or a good story." I guess Type II Fun is the good story. I imagine this guy's friends and probably he himself will consider this Type II with time!
I don't know, but my guess would be Type III Fun is where you are having fun while you're doing it, but afterwards you realize it was miserable and would never do it again.