Yes, Gangnam style is written by Psy and Gunhyung Yun. Two people are written this song.
Specifically his latest title (Gangnam Style) is K-Pop, so basically the Korean equivalent of our Pop.
However like other music artists, they don't specifically stick to one genre. They could make a pop song, then their next song could be smooth jazz.
to be honest, it may be possible that the gangnam song is the only one he made and it could be months before a new song comes out.