Right now, the U.S.'s main export is entertainment in one form or another, and a large portion of our sundry and household goods comes from China. Was there a country or culture in history that did something similar? Thanks in advance!
Right now, the U.S.'s main export is entertainment in one form or another
No, this is not even close to true. You're vastly underestimating how much stuff the US exports.
Here are the numbers. Looking over that list for 2014, here are the things that could reasonably be included under the term of cultural exports:
Add it all up, and you've got $31.5 billion out of a total of 1.620 trillion exports, or roughly 1.9%.
I don't know about culture being the primary export, but perhaps you could look at ancient Greece. The culture of the ancient Greeks was quite popular among non-Greeks around the Mediterranean. Sometimes it is even referred to as a verb - hellenisation.
Different ancient societies took things from the Greeks, such as art motifs and styles, values and activities of the aristocracy, and even borrowed myths - like how Rome was founded by Aeneas and fleeing Trojans.