You are compared with 99 other people chosen randomly. If you are better than everyone else in a specific domain, you win 1 million €/$. What do you choose?
It doesn't state it would just be one game, nor that you would have to win, just that you had to be better, which is easy to demonstrate with a program that measures the error level as backgammon is a game of skill with a large chance factor and not a game of chance.
Apart from the fact some enlightenment on the subject is only a simple query away, you can also test yourself whether there is skill is involved. Just download a free backgammon program like gnu backgammon and play the computer on the easiest setting a couple of times. You will get destroyed. Also, if it were about luck, you would have a completely random world champion every year instead of recurring winners. Not that you would care because you chose not to educate yourself and make an asinine comment anyway on a subject you clearly know nothing about.
I know it is not based on luck but luck does play a factor. Good players do lose to worse players and actually more often than in games like chess. Its exactly like poker. Sure its a game of statistics and calculated risks but its no risk if it can't fail. My point is, i wouldn't place a 1mil bet on my opponent not getting doubles more often than me over one game, or me messing up over 2 games. Let alone assume that no one else would be good at it.
Arguing that you are the best overall player without having to win a game or prove it in any way is just a weird way of trying to win this discussion.
The question doesn't state anything about a game or amount of games, just that you will be compared. Of course there is variance, but that's not what is being measured. All I'm saying is that if you take 99 random people and me, I'm fairly sure that I would be the best backgammon player.