This is better described as a tragedy of the commons, not a prisoner's dilemma.
It is a collective action problem, which is really a type of prisoner's dilemma.
https://en.wikipedia.org/wiki/Tragedy_of_the_commons
A tragedy of the commons is ALSO a collective action problem, but is not the same kind as what we are seeing here.
The commons here is an abstract one: it's the lack of incentive within a society to perform a kidnapping, which is a shared benefit/resource.
The family of the victim who decides to pay the ransom is taking from this commons (by decreasing the lack of incentive), making everyone worse off in expectation, in order to benefit only themselves and the specific victim they're trying to help.