What is the relevance of the Sandy's story about the soothsayer in The Westing Game?

The tale of the soothsayer who died laughing is Sandy’s way of telling Turtle that he is Westing.

There are many hints that Sandy McSouthers is actually Sam Westing.  First of all, his names are all directions.  He is Northrup, McSouthers, Eastman, and Westing.  As McSouthers, he has contact with the players of the game and tells Turtle the story about the soothsayer who predicted his own death as a way of telling her what is really happening.

That day came, and the soothsayer waited to die and waited some more, but nothing happened. He was so surprised and so happy to be alive that he laughed and laughed. Then, at one minute to midnight, he suddenly died. He died laughing. (Ch. 15)

Turtle tells Sandy that this is very profound.  She says nothing else.  Turtle is a smart little girl.  Sandy obviously knows that.  The purpose of the Westing Game is not just to get to know the heirs, but to have fun.  He is laughing at them.  He is not really dead at all.  He is watching them all the time.

By the time of the soothsayer story, Sandy is basically admitting to Turtle that he is messing with everyone.  She is the one who wins the game.

He was smiling. He wasn’t angry with her, he was smiling.

"Hi, Sandy,” Turtle said. “I won!” (Ch. 27)

Westing created an interesting game, got to know his heirs and the people in his life, and spent some diverting months. He showed Turtle that he had a sense of humor, even if no one else figured it out.  From then on, Turtle and Westing were very close.  She was his heir, and carried on his legacy of being very successful and having a good sense of humor.  Westing may not have died laughing, but he died happy.