I think you can attack this question from two angles: characterization and symbolism.
From a characterization perspective, the opening scene of any story is vital because it introduces the characters and teaches us, explicitly and implicitly, about their traits. In W.W. Jacob’s tale, “The Monkey’s Paw," the introductory scene begins with a chess game between Herbert and his father Mr. White. The father loses the game because he puts his king into “sharp and unnecessary perils.” Through this contest, the reader learns that Herbert is careful and methodical, while Mr. White is reckless and emotional. This information is vitally important as the plot grows darker with the revelation of the mysterious monkeys’ paw talisman.
From a symbolic perspective, the strategic game of chess often represents life. If you view the chess-game between Herbert and Mr. White from this lens, the opening competition foreshadows the carelessness with which Mr. White will treat his three wishes. Viewed symbolically, the chess game is almost allegorical: Mr. White treated his king with negligence and lost the game; when he treated the monkey’s paw carelessly, he lost his son. I hope this helps!