The theme of "Race" relates most strongly to the "Fate and Free Will" theme of this story. Given the protagonist's circumstances – as an African-American man in America before the Civil Rights era – his race has frequently defined his life opportunities and circumstances. "King of the Bingo Game" depicts the protagonist on a night that he vividly recalls the racial oppression he has been experiencing. The protagonist is able to momentarily escape his past and his situation by becoming "King."
When the protagonist is talking about showing the whole world how to win, he is talking about showing the whole world how to transcend the narrow categories of race.
The protagonist feels completely disconnected from other African-Americans.