Adueñas comes from the verb adueñarse, meaning "to take ownership of" or "to make something one's own." It's a less common verb than simply "to have" or "to possess," making it more impactful.
In the song, the lyrics "con un solo beso te adueñas de mí" (with just one kiss, you take ownership of me) beautifully express how completely the singer is captivated. It conveys a sense of being utterly taken over by love, highlighting the power of a single kiss.
Ramón Vega and Carin Leon team up for "Dueño de Ti," a song that's all about being completely, utterly, and maybe a little obsessively in love! Our singer is so smitten that he promises to "gritar a los cuatro vientos, 'te quiero'" [shout to the four winds, 'I love you']. He's ready to give his all, confessing that with just one kiss, he "pierde la razón" [loses his mind].
He's gone from being a "donjuán" [womanizer] to someone who's totally devoted, declaring, "Soy tu esclavo, soy tu mandadero, soy tu gato, soy tu pistolero" [I'm your slave, I'm your errand boy, I'm your cat, I'm your gunslinger]. He even calls himself "el perro que sigue tus pasos" [the dog that follows your steps] and "el mendigo que solo con un beso se convierte en mucho más que eso" [the beggar who with just one kiss becomes much more than that]. It's a fun, over-the-top declaration of love, showing how one person can completely change your world and make you want to be their everything, just to be "el dueño de ti" [the owner of you].