Actually, it's not aiming at protecting local music industry, if so they would do that years ago. It's more like to push political/business pressure on South Korea to stop them installing THAAD.
It is always hard to tell why they do things. The pretext is...retaliation, but they look at all the other wins, and protectionism has a lot to do with it. Heck, Korean dramas were getting way too popular for local media comfort before the THAAD cut backs.
S. Korea is also a democracy. The regime is highly suspicious of any foreign culture which might make people more interested in control of their own government.