Gozo can mean "joy" as a noun, but in this song, it's used as a verb, meaning "I enjoy" or "I revel in something."
It's an interesting word choice because it's less common than disfruto (I enjoy) and carries a slightly more intense, almost spiritual, sense of enjoyment or pleasure. The repetition "Ay, cómo la gozo, ay, cómo la gozo" emphasizes the deep satisfaction the singer feels, adding a memorable and unique flavor to the lyrics.
This song, "Blanca Y María," by Codiciado and Fuerza Regida, tells a really fun and a bit chaotic story about a guy who can't seem to choose between two women, Blanca and María, and maybe a third, his main love interest. He starts by admitting, "Por culpa de Blanca no me fui contigo" [Because of Blanca, I didn't go with you], suggesting Blanca was a distraction. He also mentions getting drunk and ending up with María to avoid feeling lonely: "Me llevé a María pa' no sentirme solo" [I took María so I wouldn't feel alone]. He even says, "Ay, cómo la gozo, ay, cómo la gozo" [Oh, how I enjoy her, oh, how I enjoy her], which is pretty blunt!
Things get even more complicated as he tries to explain himself. He remembers the morning after with "Los botes abiertos y olor a Marlboro" [Open cans and the smell of Marlboro], and "Llamadas perdidas y un corazón roto" [Missed calls and a broken heart]. He blames his main love interest for the situation, saying, "Pero fue por tu culpa" [But it was your fault], and then tries to explain his reasons for not being able to leave Blanca and María. He says, "Cuando ando con Blanca, pego de suspiro" [When I'm with Blanca, I sigh] and "Cuando ando contigo, me siento tranquilo" [When I'm with you, I feel calm], showing how different they are. He even claims, "sin las dos me muero" [without the two of them, I die], which is a pretty dramatic way to say he needs them both! It's a wild ride of excuses and affections, all wrapped up in a catchy tune.