I don't know if you're familiar with Chinese, Japanese, or Vietnamese, but those languages as well as Korean have a wealth of words that are derived from a combination of two Chinese characters. Often you'll stick two of those together to get a compound that's four characters (really simple example is 자기소개/自己紹介, composed of 자기/自己 self + 소개/紹介 introduction yielding self-introduction). That can be a mouthful, so sometimes those four character compounds will get abbreviated by taking just the first character of each word; it's similar to how we might make an acronym in a Western language, but each Chinese character can be pronounced by itself and also carries meaning.

That's exactly what's going on with our Korean example: 미국/米國 America + 제국주의/帝國主義 imperialism (itself a combination of empire and -ism) = 미제/米帝 American imperialism. Then, we slap the native Korean word 놈 on the end which is a derogatory term for a man (e.g. bastard) to yield 米帝놈/미제놈 American imperialist bastard.