However, it is often used to accuse others of a lack thereof when the person fails to laugh at someone else's expense. Or when the person fails to laugh WITH those who are laughing AT him.
Many if not most people say "sense of humor" when they mean "C'mon, let us have a little fun at your expense."
"Albert, that fatty, fell while trying his ballet moves. We all started laughing. He didn't laugh because he has no sense of humor."