The Muslims don't seem to laugh at anything unless it has something to do with someone getting killed.
I've been giving this some thought. I lived in Saudi Arabia for three years and spent most of my time with Saudi military who spoke good English. They liked dirty jokes but got quiet when the muttawah (religious officer) came around. The muttawah is like a religious commissar. They may be lower ranking enlisted or officers but everybody pays attention. These guys have their own chain of command and can make life miserable for you.
They were also known as 'long beards' and whenever a Saudi referred to them they would cup their hand about chest level to indicate the length of the guys beard. I've seen them making that sign, laughing and pointing when the guy's back was turned.
I had very friendly relations with many of these guys who had spent four or five years training in the U.S. We made a lot of jokes about wives, sheep, camels, driving, etc. It was a rough place and the humor was pretty rough. A lot of these guys were real jokers.
I saw the entire (Muslim) staff of my favorite restaraunt get a big laugh when one of them opened the curtain unexpectedly in the 'family' section of restaraunt and accidently saw the uncovered face of an old man's young wife. He was supposed to rattle the curtain before he came in.
The old man chased him downstairs to the 'bachelor' section of the restaurant and was giving this young guy hell while my Egyption waiter was laughing out loud trying to explain to me what was going on. All the staff and patrons were smiling as this guy was going on and on....
I never got to a Saudi comedy club. I don't think there is such a thing. I can see the religious establishment not allowing it. I don't think there is anything in Saudi Arabia that is public, funny, and is aimed at adults. They take their religion to seriously.