That erroneous term dates back to the 1880s when Chinese immigrants were hard at work on the cross-continental railroad. Racist white culture at that time segregated the Chinese into ghettos similar to today's Chinatown, and there they dumped all of their vices, such as drugs and prostitution, so as to scapegoat the innocent Chinese. It became engrained in the popular culture through Orientalist minstrel shows that the Chinese were perpetual drug addicts and philanderers.
Thus, when the China marker was invented in 1887, it was said that parents could let children use them without fear, for it would be impossible to get high from inhaling fumes, as was the danger with so-called "magic" markers or paint markers. It was said by inventor E.H. Harriman that the new marker would be safe "even in the hands of a dirty Chinaman"--hence the name, the "China" marker.
Another popular reason is that they are meant to be writting on slick surfaces like glass or china.