On a warm spring day in 2012, Xi Jinping, then China’s vice president, met with Bill Gates in Beijing. As the men were walking out of the meeting room, the conversation turned to smoking in a country that consumes nearly half the world’s cigarettes. Mr. Xi, a former smoker, said he felt much better after quitting years earlier and described tobacco use as a serious problem for China, recalled Dr. Ray Yip, then head of the Gates Foundation in China. Mr. Xi, who would become president the next year, promised to “do something about tobacco,” Dr. Yip said. Days later, Mr. Gates appeared at an antismoking event with Peng Liyuan, the Chinese leader’s wife and a celebrity singer. Both wore red shirts emblazoned with an antismoking slogan. Yet in the 14 years since, as Mr. Xi has become China’s most dominant leader in decades, Beijing has made only slow progress curbing tobacco use or enacting a national indoor smoking ban.…