The short-story is an account of a title-match between two humans at a board-game that aliens taught humans. The account is by a child.
Captain someone went space-exploring and encountered aliens. They taught him a board game which seems of the same broad-type as go/weichi/baduk and othello. The story is by a child who converses with both players in a title-match (one of them is the captain) and goes on to become a champion himself.
Two bits come to my mind. The challenger plays a move and the captain whispers 'beautiful move' and calls a break, though the story-teller says that it would have been mundane by modern standards. Another bit is when one player says that the white pieces and black pieces are the same, just different colours.