Igualito is a diminutive of igual (same), meaning "exactly the same" or "just like". It adds an emphatic and often colloquial touch that you don't always find with the simpler igual.
In the song, Jesse Baez uses igualito to express a cynical realization: "Sé que a todas las trata igualito que a ti" (I know he treats all of them exactly the same as you). This word choice highlights the protagonist's bitter understanding that his love interest is not special to the new person, making it a poignant and memorable word in the context of the lyrics.
Jesse Baez, a Guatemalan artist, teams up with Naked Geometry in "Apaga La Luz" to tell a story about a relationship that's gone cold. The singer feels his partner has changed, saying, "Porque ahora eres mala conmigo / Desde que volviste siento frío" [Because now you're mean to me / Since you came back I feel cold]. He senses distance, even wondering if it's their "última noche contigo, girl" [last night with you, girl].
He desperately wants to go back to how things were, pleading, "Apaga la luz / Déjame amarte como antes" [Turn off the light / Let me love you like before] and "Déjame empezar de cero" [Let me start from scratch]. He's frustrated because he feels ignored, asking, "Sino me vas a contestar girl, y en lugar de ver tu celular / Apaga la luz" [If you're not going to answer me girl, and instead of looking at your phone / Turn off the light]. The song also has a blunt moment where he asks about another person, "Cuéntame qué ha hecho el man para ti" [Tell me what that guy has done for you], showing his insecurity and suspicion about who might be making her happy now.