The way I see it, "Princess" is just a title.
In the original timeline, then yes, I would have believed that Shao Kahn had a sort of fatherly love for Kitana, hence why he kept her by his side after Sindel's death. He trained her to become the ultimate assassin and was kinda a prize that he showed off to people, like "I killed her people and took her lands, yet she is completely loyal to me and kills whomever I tell her to without question!".
However, in the new timeline, Shao Kahn even tells Kitana that he doesn't know why he even bothered to keep her alive all these years. He holds no love for her, because she is just another disposable minion. He doesn't see her as his daughter. She's just another slave under his might. People just continue to call her princess, because that is what they are lead to believe she is, that she really is Shao Kahn's daughter, but in reality, it's just a title Shao Kahn has given her to keep up appearances. She's just a doll he dresses up, so to speak.
Her entire life is a lie. She holds no true rights as a princess while under Shao Kahn's rule. But as an assassin, she's feared and has 10.000 years of training and killings behind her. Hence why I say she is an assassin first and a princess second.
That's just my theory though.
I DO hope she will at some point free Edenia in the new timeline and rule it as its queen, gaining her true heritage as royalty.
