The 27-year-old from Chennai, who won the Winnipeg Winter Open trophy -- her maiden WSA world title in February this year -- lost 3-11 8-11 11-8 5-11 against her third seeded opponent at the Scotstoun Campus.
King, who had won a silver and a gold in Delhi Games, started on an aggressive note winning the first two games. Chinappa tried to make a comeback and pocketed the third game but the New Zealander put it across the Indian in the fourth round comfortably.
Among other Indians, Dipika Pallikal, Sourabh Ghosal and Anaka Alankamony will play later in the day.
India has not won a squash medal since the sport's inception in the CWG programme in 1998.