The g-slur goes back to the Spanish-American War and then the Filipino-American War. Americans in the Philippines thought Filipino languages sounded like "guk guk buk buk" the same way they think Mandarin is "King Kong ling long." It got shortened down to come up with the slur, which became more widespread when the Philippines tried to gain independence.

And because Americans are so racist, they used the same slur against Koreans and Vietnamese as though Asians are all interchangeable. Doesn't surprise me they thought "miguk" was Koreans using the slur in a "Well of course they call themselves that! They recognize the superior white man," kind of way.