What is the "socket" on Hirose DF13-series jumpers?
The part where this pictured thing goes to is called "housing", see, for example, Digi-Key search for "Hirose DF13"

All information is already in the link you provided. The bottom shows an example of 3-pin "socket housing". Clicking on the provided image leads you to the housing itself, and the bottom gives you a list of mating products.