The original paper discusses this in more detail. There is a well understood phenomenon called sperm paratism where male sperm will take over the egg, instead of sexually reproducing with the egg.
In sexual reproduction the offspring has 50% of its genetic material from both parents. In sperm parasitism the offspring is 100% related to the male and the female’s genetic material has been destroyed.
These inbericus females are allowing the messor male line to reproduce by sperm parisitism to maintain a domesticated messor line that they can then later sexually reproduce with to create hybrid worker ants.