Actually, it's just a matter of word choice. He was referring to the 'god' of 'many gods' (polytheism) instead of the one and only God of the Semitic religions. That's why it's written as 신 (a deity) instead of 하나님 (the one and only God, 하나 means one), so when translated it resulted in a small 'g' instead of capital. I think it's the same in English, the 'god' of many 'gods' or 'goddess' in polytheism is always written in a small 'g', because there's none that's considered more powerful than the others, unlike the true one 'God' who controls everything, I guess.
He said "운이라는 걸 주관하는 신이" which means "a god who controls luck", because in polytheism every god has their own role. To be very honest, many people, especially non religious people or atheists in South Korea are confused between polytheistic gods and monotheistic God, many doubt the existence of God because of this.
Historically, the traditional religion of South Korea is Shamanism, before Buddhism came along. Both religions believe in many deities, as in 'gods' or 'goddess'. Buddhism (polytheism) is the major religion now, hence it has many influences on Korean culture. However, there are more irreligious people than the religious ones, it's hard for them to accept and to differentiate the concept of polytheism and monotheism, so this is where the 'indifferent' attitude (like what JYP said) came. Either he doesn't believe in the concept of the higher power, or he's just confused because his culture is very influenced by polytheism, but the current wave (I can't find the right word) in SK goes towards monotheism. I think this is also happening in the Japanese society "Born Shinto, Marry Christian, Die Buddhist" (Kisala 2006: 3).
I'm not saying that monotheism is new in SK, but in terms of Christianity and other monotheistic religions, it's new. Christianity entered SK near the end of the 19th century. Although, there's an assumption that Koreans were monotheistic long before they encountered Christianity (this is a rather interesting paper if anyone is interested: http://rinks.aks.ac.kr/Portal/ContentsView?sCode=LIBRARY&sId=302793). In conclusion, what JYP stated about 'god' and 'God' (he used both of the terms), could be because of his confusion and his indifferent attitude towards religions or the concept of the higher power.
