It's playing off the fact that the plural for persons from China and the adjective to describe things that are from China are the same; it's essentially a pun.
Americans can eat Chinese because we often refer to cuisine by its preceding adjective and allow the noun to drop implicitly. Similarly, you'd see "Americans can eat Indian" or "Americans can eat Mexican". In all cases, the implication is "Americans can eat Chinese [food]", or "Americans can eat Mexican [food]"
Chinese can't eat Americans because "Americans" isn't an adjective anymore but a plural noun. Chinese would simply eat American. As with the prior example however, you'd never see "Americans can eat Indians" or "Americans can eat Mexicans". (And Americans eat American all the time as well!)
TL;DR It's a pun on the peculiar homophones that can result from certain demonyms which, in english, don't take on a standard plural form. Other examples would include Japanese, and British