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This "game" term, part of a mental challenge that Ender faces in Battle School, is a “choice” the player must make (see Chapter 6).  Unfortunately, in this either-or game, whether the player chooses the drink or doesn’t, he dies.  It is one of those paradoxical or enigmatic false choices that philosophers sometimes construct, to make an abstract point.  The Prisoner’s Dilemma is another.  One of the earliest is Zeno’s paradox about the turtle that never can get to his destination because it can never get more than halfway to it.  Possibly the most famous is Schroedinger’s Cat, which cannot be pronounced dead or alive.  Ender uses some “out of the box” thinking to win the game, thereby again demonstrating his intelligence, as well as his leadership skills.  The solution to the Gian’t Drink puzzle foreshadows Ender’s final realization in the book, in that the Bugger solution is not to kill the Buggers but to learn from them.