The Game of Life is a location in Problem Sleuth. It is an imaginary world within the imaginary universe that manifests itself through a board game suggested to by Death. The irony of this game falls flat on Ace Dick, who is asked to play this game with him atop of DMK's hat.
True to his hard-boiled ways, Ace Dick steals Death's money and runs off with it and continues to play the game outside the boundaries of the rules, eventually finding Wifehearst and having a son — sweet, sweet Sonhearst.
The second ironic part of this game is that while the events that progress are equally absurd and even more outside the rules, such as engaging in other game situations such as Oregon Trail, it still evokes the essential aspect of gameplay—that your life ends up not always being the way you wanted. This knowledge blows Ace Dick's mind apart when the game ends.
And if there wasn't enough irony, after his game of Life, Death shows up to bring him to the Afterlife to save his life before they fall off of DMK's hat.
Weird puzzle shit sure can be confusing sometimes.