Honest question, what's the meaning behind this joke? Is it just referencing the fact that American English drops "u" in the spelling of e.g. "color"?

It's primarily a reference to various language selection dropdowns offering "Chinese (Traditional)" (which is used in Taiwan) and "Chinese (Simplified)" (which is used on the Chinese mainland). That difference arises from Mao-era simplification of many of the most common hanzi characters to make them easier to write or distinguish.

Mixed with, yes, the variant spellings and word choices (e.g. chips/crisps/biscuits) that make it apparent to British English readers when something is American.