The indictment by South Korean prosecutors of a Japanese journalist on a charge of defamation for an article he wrote about President Park Geun-hye highlights questions about press freedom in Korea as well as a micro-industry of gossip that centers on the nation’s financial sector.

Tatsuya Kato, a former Seoul bureau chief for the Japanese media outlet Sankei Shimbun, detailed in an Aug. 3 online-only report a column carried in South Korea’s largest circulation daily, the Chosun Ilbo, that questioned what Ms. Park was doing...