As a pastime that involves strategy, risk and surprise, the game of chess mirrors life in those very aspects. Those who love the effervescence of risk often put themselves willingly in dangerous situations which can lead to radical options: life or death, sanity or insanity, safety or lack thereof. Since this scene takes place at the very beginning of the story, it is safe to conclude that it foreshadows another dangerous and risky situation that will equally involve life and death in a way that is similarly done in chess.
This opening scene is described as follows:
Father and son were at chess, the former, who possessed ideas about the game involving radical changes, putting his king into such sharp and unnecessary perils that it even provoked comment from the white-haired old lady knitting placidly by the fire.
This settles the notion that Mr. White revels in risk-taking behavior and loves to provoke fate, to a point. He enjoys this aspect of risk, and he does not seem to acknowledge that for every action there is a consequence.
When his turn comes to wish upon the monkey's paw, he will display the same behaviors that he does at chess. He is reckless and does not think about all the possible consequences that come from "playing with fire". As such, death will come as a result of his behavior. This is a cautionary tale that tells us that we do not have any control over things, and that we should never tempt fate.