B-King is a gangster and a leader of B-King gang. His full name is Keisuke Baba.
Yakuza 1 Chapter 6: Fatherhood - Takashi is trying to leave the gang he's got embroiled in. The gang try and persuade him to stay with threatened violence, but Kiryu beats them and their leader known as B-King. B-King says that Kyoka Atobe stole the Family's money so they are after her.
Kiryu substory - The Twist is Back in Style - Kiryu receives an anonymous email from "twisted curve". On visiting the Yoshida Batting Centre a weird man tells Kiryu that back in Yakuza 1 Chapter 6: Fatherhood, he called him "Twisted Curve" when he got into a fight with him. He was the B-Kings leader at the time. He reveals himself as Keisuke Baba a Major League baseball player.
Keisuke believes Takashi made the wrong choice all those years ago and that Kiryu made him out to be the bad guy. He explains that thing we think of as "right" boil down to nothing more than personal opinions of the powerful. By attaining success he therefore proves that he made the right choices up until now.
On successfully hitting his pitches, Keisuke asks his Agent, Mike, to book him tickets so he can go off on a journey and perfect his pitch. He tells Kiryu he'll be back someday and will beat him.