He didn't necessarily have to "throw" the match, per se. As others have said, a 55-year-old man, even a Grand Slam champion, is not going to have the strength or stamina to hold up to a full match against a world-class tennis player at her peak, even if she is a woman. Even if he had made a deal with the mafia, it would not have taken much effort for Riggs to "let" King beat him soundly. Riggs was just too old.
In fact, the age difference was about the only thing that made this contest a fair fight. Among peers, the man would win almost every time (Riggs actually did beat Margaret Smith Court a few weeks prior, and easily). It would be like putting Pele and his cohorts up against the current U.S. women's soccer team.