When using sterile mosquitoes, the idea isn't that they pass on their genes, but that they dominate mating and therefore disrupt the breeding cycle. I.e. you release LOTS of sterile males and the normal females spend time mating with them instead of normal males and the population therefore decreases (until you run out of sterile males).

I think the better option (also in the article) is to release engineered males that result on male only offspring. Eventually you run out of females and the species dies off.