I don't see any real justification to call it the American Empire since it's not built on Imperial Conquest. There is no Emperor. People use the word hegemony incorrectly. The eagle has "hegemony" over the rat because of Evolution, not something the eagle plotted out. Likewise, American popularity and mutual relationships are because of our inventions whether its computer chips, smart phones, movies, musical forms, software (like this platform or the actual software languages themselves such a C and javascript and Swift that run this platform). And speaking of languages, the English language is popular because its powerful and useful and borrows from nearly every language and has a sort of average sound to it. This is the most powerful hegemony of all because it's the currency of ideas. You won't see people running out to learn Chinese or Russian any time soon outside those countries. We don't need 5,000 new Chinese characters to learn, 26 letters and emojis are enough, another American invention.