Engañe' is a colloquial, shortened form of engañes, which comes from the verb engañar (to deceive).
In the song, the lyric "Ya no te engañe', ella lo quiere" means "Don't deceive yourself anymore, she loves him." It's a direct and impactful phrase, urging the listener to face a difficult truth about a past love. This word is interesting because it's used in a very common, conversational way, making it feel authentic and relatable.
The whole song is one man talking to another about the woman they have both loved, and it hides its twist until the final line. He opens gently — "Ese hombre no quiso hacerte daño" (That man didn't mean to hurt you) — then relays her side of it: "Cuéntale que estoy muy bien" (Tell him I'm very well), "Que fueron muchos años de soledad" (That there were many years of loneliness). The other man keeps cutting in, first pleading "Convéncela" (Convince her), then refusing to believe any of it: "Sé que él le mintió" (I know he lied to her).
Then the speaker names himself. "Porque ese hombre" (Because that man), "Ese hombre soy yo" (That man is me). Everything before it re-reads as a confession dressed up as consolation — the advice to let her go, the insistence that she is happier now, the stranger accused of having stolen her. Miranda! and Abraham Mateo sing it as the two-hander it was written to be, by Joaquín and Lucía Galán of Pimpinela, over a synth-pop backing that turns the argument into something closer to a dance than a fight.