Hi there Cecil!
Usually, I agree with most of your explanations about these mysteries of life, but your explanation of D&D was obviously cursory and glib.
Dungeons and Dragons is a complicated game, granted, however, it is a game with a difference.
Some pertinent points:
A: D&D, and roleplaying in general does not involve winning or losing, but accomplishment and problem-solving. For kids age 12 to 17 this is a good thing. in the hands of a proper moderator they can learn self-reliance, honor, responsibility, critical- and analytical thinking. It also involves a concept of result for action, with the consequences of unwise actions being"dire" (but not really!) The concept of “risk” creates an aura of excitement like any game, and the outcome is not always certain, even to the referee.
B: The Math involved, though at first daunting, is not anymore. The original editions of D&D were at first a bit like the Income Tax Long Form! Now, though, a new company has now produce the 3rd Edition, which is much simpler. But, what’s the problem with math, huh? The U.S. is one of the lowest rated countries as regards education, math being the worst.
C: “To play D&D you need at least two acolytes, who play under the guidance of a vaguely Mansonesque personage called the Dungeon Master (DM).” This I find very insulting. I am a 32 year old, educated, professional. I get together once or twice a week with five or six people of the same type, intelligent, normal people. We create a story, a movie of the mind if you will. We explore moral quandaries as well as current political themes with our characters as the “stars”. I refer to the Dungeon Master as a “moderator” “referee” or even “director”. This is the true purpose of a DM, as an arbiter in play situations where the outcome is unsure. With dice as a random factor, any situation can be played out to everyone’s satisfaction as to fairness.
Obviously, your research did not actually include “playing” the game. I invite you to find anyone who will, to let you play as research and then write another answer.