This would often be recited by children as their fingers were used to pull up at the sides of the eyes so as to make them
slanted. Variants include turning the rhyme into a question: "Are you Chinese, Japanese, or Dirty Knees?" and "Are you Chinese, Japanese, or Americanese? You must be Dirty Knees."
Considering the whole of the Asian continent besides China and Japan would be lumped under "dirty knees," you would think the Chinese or Japanese would be grateful to be excluded from that classification. To an Asian child, however, this really doesn't matter much. To an Asian adult as myself, this racist children's rhyme is merely a reflection of society.
It's somewhat amusing that this should be no more than a mere pointing out of the difference in physical characteristics between Asians and Caucasians. Still, the rhyming nature and eye-slanting is rather offensive in its taunting like a Vapors video. As much as I would like to ascribe it to children who see only the physical differences and nothing more, the fact that this meme has spread so far requires a widespread dissemination factor to explain it. And that is what makes this more nefarious.