Yes of course. The family of the kidnapped victim has power.I get what you are saying, but by the very notion that a transaction needs to occur, and the other notion that it is not an automatic transaction, there is power on both sides. I'm not saying that there isn't a strong and often emotional motivation to appease a kidnapper's requests, but if it was complete power on their side, it would have been paid the minute the ransom note was received. Each party wants something, and negotiation is the process whereby each party tries to get their needs met. This is very obvious in the last video of the family.
The perception that they have full power is exactly what they WANT their targets to feel. But in reality, they don't have all the 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.