There are two types of dharma kings, worldly dharma kings and true dharma kings. Worldly dharma kings are so named by worldly sources while true dharma kings are so designated by the Buddhas and have the full power of the Buddha-dharma with which they can help living beings.
See H.H. Dorje Chang Buddha III and “Listing of Famous Dharma Kings” from True Stories About a Holy Monk. Worldly rulers like King Ashoka who ruled according to the principles of Buddhism are also referred to as “Dharma Kings,” but that is not what is meant here.