Derechos literally means "rights." While it's a common word, its use in the phrase "amigos con derechos" (friends with benefits) makes it particularly interesting and unique to this song's theme.
In this context, it refers to a relationship where two people are friends but also engage in a romantic or sexual relationship without the commitment of a traditional partnership. This phrase is a widely recognized idiom in Spanish, and understanding it unlocks a deeper meaning in the song's narrative about a complicated, non-exclusive relationship.
The narrator knows exactly where he stands and asks for the lie anyway. He opens with Mienteme como tú sabes (Lie to me the way you know how), Porque de eso ya me acostumbré (Because I'm already used to that). She is with someone else, which he says out loud by the third line, Aunque tú estés con él (Even if you are with him), and he calls her at night regardless. There is no plea for her to leave the other guy. What he asks for is the secret itself, Que me escondas de él, me vale (I don't care if you hide me from him), and a better place in a queue he already knows he is standing in, Súmame más a tu lista (Move me further up your list).
Halfway through, the song stops for twenty seconds of shoutouts, Peso Pluma and Pedro Tovar naming each other over the guitar, and then the second verse explains how the two of them got here. Es que yo ya te perdí la fe (It's just that I've already lost faith in you), De que nunca, nunca tu novio seré (That I will never, ever be your boyfriend). So they made a deal, and the deal is the title: Llegamos a un buen acuerdo (We reached a good agreement), De ser amigos con derechos (To be friends with benefits). The small blunt dig he drops in the middle of explaining it, Tus tipos son vatos flacos (Your guys are skinny dudes), is a good sign he has not made his peace with the arrangement quite as thoroughly as he claims.