Desvelado is an expressive word for being sleepless or sleep-deprived, usually from staying up very late. It comes from the verb velar, which means 'to keep watch' or 'to stay awake'.
In the song, the singer laments, "por tu culpa me la paso desvelado" (it's your fault I'm always sleepless). He uses this word to capture the romantic angst of losing sleep while waiting for a late-night call from someone, a very relatable and dramatic feeling.
This song is a super catchy and honest story about being the 'other guy'. The singer knows exactly what's going on with the woman he's seeing. He opens by complimenting her, "Chula, qué bellos ojos" (Pretty girl, what beautiful eyes), but immediately asks if she's with her boyfriend, claiming he's "cero celoso" (not jealous at all). Of course, he's just being sly.
He's totally aware that she's using him to cheat. He knows she lies and he just plays along, admitting, "Dice que eso es especial, pero yo soy el otro" (She says this is special, but I'm the other guy). He even notices she's saved his contact under a different name on her phone! Despite knowing all this, he can't resist. Whenever her boyfriend leaves and she calls, he drops everything and goes right to her, even if it means losing sleep: "tú me llamas cuando se va ese pelado / Y en corto yo me jalo" (you call me when that guy leaves / And I take off right away).