https://press.uni-mainz.de/determining-sex-in-ants/
somehow a male ant has one set of chromosomes while the female ant has two sets of chromosomes. So a male ant sperm must contain enough information to make a complete male? Then when they mate with the female of the other species, the females egg actually gets blanked out so to speak, containing none of the females own genetic material. Then the male sperm fertilizes the egg with one set of chromosomes producing a male offspring that is a clone?
In normal ants, the queen can produce haploid (single set of chromosomes) unfertilized eggs that hatch into males. Normal ant males are haploid. They don't have a father, they can not have sons (but the do have a grandfather, and their daughters will make them grandsons). When the ant queen decides to produce sons, she will make haploid eggs via meiosis as normal, and just won't fertilize them with male sperm.
Ants don't have sex chromosomes. An individual with a single set of chromosomes (haploid) is a male, an individual with double set of chromosomes (diploid) is a female. Ant males are almost like sperm cells that grew into multicellular organisms.
https://en.wikipedia.org/wiki/Haplodiploidy
Now, a Messor ibericus queen can produce eggs with her own genetic material removed, and fertilize these with the single set of chromosomes from a Messor structor male. (It will still have the mitochondria and mitochondrial DNA from the queen.) And because the male only has a single set of chromosomes, the sperm and the resulting offspring has an identical single copy of the father's genetic material (except the mitochondria that came from the mother). So the son is a clone of the father (except for mitochondria).
The queen can also mate with males of her own species, contributing half of her own chromosomes to combine with the full single set of the male chromosomes, to produce to-be-queen female offspring. Here we have the normal genetic recombination (though only on the mother's side) to keep the evolutionary benefits of the variation from sexual reproduction.
The interesting part is whether M. ibericus queens do actively remove their own genetic from eggs fertilized with builder sperm. Why would they do this?
M. ibericus queens produce ibericus×structor hybrids as infertile female worker ants.
M. ibericus queens produce structor males, so future queens can keep producing the hybrid worker ants.
My guess is, maybe there is some benefit having the workers to be hybrids and not pure ibericus ("hybrid vigor" [1]). So it's worth the effort of keeping the structor males along, to be able to produce the hybrid workers. But I think the pure ibericus genes in the line of queens are in control.