What does ender accomplish in the giant's drink game at the end of chapter 6?

Ender plays the "mind game" and generally does well, but the game always returns to the Giant's drink. Although he figures out that the choice is pointless, Ender keeps returning and trying to find ways to beat the Giant, because the Giant talks about a "Fairyland" that the players can go to if they beat him. Finally, Ender kicks over the two glasses, jumps into the Giant's face, and digs into the Giant's eye. Eventually, the Giant falls over dead, and Ender reaches Fairyland. A bat flies up and notes that "nobody ever comes here." Ender worries that even in the game, he is a murderer--"Peter would be proud of me."