I don't like this kind of music.

Literal

I [topic-は] this-kind-of music [subject-が] not like.

こういう ('this kind of') is the colloquial counterpart of the slightly more bookish こういった. The が-marked subject (rather than a contrastive は) makes this feel direct: music as the grammatical subject of dislike, not a hedged topic. 好き takes が for the thing liked or disliked — a recurring pattern with adjectives of preference and ability.