No, it's referring to the tableware -- every word in that position for all the phrases is a container of some sort (or at least a thing that can contain other things).
Come on, there's reasonable (n words would probably not be the greatest even in an insult generator), and then there's what you're complaining about. China is a country that is viewed negatively by most of the western democratic countries. And for a good reason. If you equate China with Asian, implying racism, that is your own bias speaking.
Probably reasonable people would differ on whether unfavourably viewed (by the West) countries, such as Iran, Cuba, Palestine, or Saudi Arabia are disliked for good reason or not.
I agree with other comments that “China” in this context is intended to refer to porcelain. However including “Persian” (rugs?), “Cubano” (cigars?), “Afghan” (dogs?), or Arab (numerals?) as nouns in your cute online insult generator is probably a bad idea.
Edit: I see that “Boston” and “English” are also included as insults. At least with those there can be no doubt.