I think it's a similar error that other user already posted(Cyrillic characters in Browser print are not showing correctly. )
A Zebra staff answered the post that they already recognized and was working on the issue with certain multi-byte characters, and probably work is not done yet.
And I want to give them more information that might be helpful if they didn't know about Korean characters' problem.
 
^XA^CW1,E:corefont.ttf^CI26^SEE:UHANGUL.DAT^FO80,200^A136,36^FD박찬호^FS^XZ
 
If I send the above ZPL command directly to the printer using zebra tool it works fine, but if I send the very same command through browser print, than it prints weird characters.
In the picture, first label is printed by browser print, in which 박찬호 had to be printed but 갔?, and the second one is by Zebra utility.
I used browser print sample from the installed directory, and only thing I changed was assigned value of format_start of DevDemo.js(line 5).
(var format_start = "^XA^CW1,E:corefont.ttf^CI26^SEE:UHANGUL.DAT^FO80,200^A136,36^FD";)