The battle between two gambling titans ended with both men in the twilights of their careers defeated and ousted by the companies they built.

Casino magnate Steve Wynn and Japanese pachinko king Kazuo Okada had teamed up to rebuild Mr. Wynn’s gambling empire, Wynn Resorts. Their relationship ended when Mr. Okada was ousted from the Wynn board and his shares were seized by the company.

While...