Why is Greek music being exported so successfully to outside markets like the Balkans, Turkey and the Middle East?

Because it is damn good.
For example Rebetiko - Wikipedia (https://en.wikipedia.org/wiki/Rebetiko). You hear some Bouzouki - Wikipedia (https://en.wikipedia.org/wiki/Bouzouki) and it suddenly gives you goose bumps. In Albania it is quite popular in particular in the South.
Not only music but also dances that are derived from it are just amazing.
For me Greek music was a good reason to learn Greek language or better say it helped me to learn the language.
My favorite singer?
Notis Sfakanakis. “Soma mou, apopse pali nikises” or (Η Κιβωτός) “γεννηθηκα στη κιβωτος 9 και 13” .

To answer your question, half a million (economic immigrants) Albanians in Greece keep exporting Greek music in Albania. Together with some Greek dishes such as musaka.
Finally, I don’t know about Middle East or Turkey but I guess that music as a form of cultural contamination finds unexpected ways to travel.