A district court at Suweon south of Seoul sentenced the husband to two years in jail, but suspended the wife's two-year jail term since she is pregnant with a second child.
"The defendants' prematurely born daughter needed constant care but they did not feed the baby and even beat her, while indulging in online games," the court said in a ruling.
"This constitutes an inhumane and anti-humanitarian crime which cannot be forgivable under any circumstances."
The case shocked South Korea. The following month the government announced tougher rules to combat Internet game addiction including a "fatigue" system encouraging players to switch off.
Under the new rules, three major game operators will have to introduce a shutdown programme from September and younger users will be limited to a time period set by a parent or guardian.
In March a 32-year-old man died after reportedly playing for five days with few breaks. A similar incident involving a 28-year-old man occurred in 2005.
Official data esimates that the highly-wired nation has two million web addicts, representing almost 10 percent of total online users.
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