Even though the developer says that Sophia has control in the Casino Story I believe he means that the player has choices within the story. Day 01 of the game Liam is the protector, provider and an aesthetic for Sophia (in spite of marginal romance.) Liam's provider quality has been slowly eroding since Sophia called him to find her car keys. Sam steps in and finds her keys, goes shopping with her and carries her groceries for her. Sam further grows as a provider figure during the guitar and cello lesson (although his provider role is still small.) Sophia's eroding impression of Liam as a provider is devastated on playable day 09 when he losses a third of the house value gambling. I don't believe it is a coincidence that earlier that same day Sophia's attempts to handle Aiden through the school authority and the legal authority both fail. Her structured environment with established rules and unquestioned authority has collapsed. She needs a protector, and does not go to Liam. Her failure to approach her protector begins the collapse of his second role as well.
Playable day 10 we see Sophia confiding intimately to others to fill her need for holes in Liam's role for her. She allows Ellie to see her front in the shower, and admits to her dead sex life. Sophia is aroused by her unbuttoned blouse in class, accepts a kiss from Emma and even shows Dylan her breasts. When Dylan defines MILF for her, she actively fantasizes about people she knows. The transfer of affection from Liam is graphicly displayed by the bikini show.
During the meeting with Morello, Liam is completely disrespected and Sophia no longer sees him as her protector. There is no blackmail required because Liam's destruction is already done. Sophia will now seek a strong masculine presence elsewhere without need of coercion because there is no control left.