Xenophobia is about prejudice. The joke in question relies on underlying prejudice towards the image of Chinese restaurants in America in order for the joke to land.

If you don’t understand the stereotype of Chinese restaurants the joke wouldn’t be funny to you.

Is it bad or legitimately harmful to perpetuate those types of stereotypes? Probably not. But I don’t think the quality of the joke makes up for it in this case.

FWIW the notion of unscrupulous food vendors serving dog/cat meat is pretty common in other cultures, and it doesn't exclusively apply to Chinese restaurants. I've heard it in just about any context where meat is served.

To give a specific example, there's an old Soviet joke about a guy buying meat pierogi from a street vendor; after closely inspecting them, he asks: "So, did this meat bark or meow?", to which the seller replies, "Neither; it asked too many questions."