Yes of course. The family of the kidnapped victim has power.
They have the ultimate power, the money.
Kidnapping is essentially a business crime. The kidnapper steals a person, and wants the family to buy that person back. The point of the kidnapping is to make money. So we have a buyer and a seller.
Yes the kidnapper may have issues around control, power, narcissism, sadism etc. And appear to have all the control especially initially. But the family and law enforcement have leverage.
The kidnapper wants the money and wants to avoid arrest. The longer the negotiations go on it is less likely the kidnapper will receive his money and the more likely he will be apprehended.
So he is under pressure too.
ETA: The power dynamics may shift back and forth.