The article in particular that you reference is discussing the possibility of using a mechanism called gene drive. The concept of gene drive breaks the normal "rules" of inheritance and allows a gene to spread much more rapidly than normal in a population.
Gene drive depends on the idea of a selfish gene. There are naturally occurring genes that make copies of themselves to other parts of the genome. Selection pressures can operate at the level of these genes: a gene that can copy itself is going to end up in more offspring than would be expected due to random assortment.
For example, imagine a gene present in one chromosome of one parent. Typically, only half of that parent's offspring will have that gene. However, if the gene is able to copy itself to the parent's other chromosome, now all offspring of that parent will have that gene. The prevalence of the gene just doubled. It's possible that the gene will also confer some negative traits, but as long as those negative traits aren't sufficient to cause a >50% reduction in later reproduction of the offspring, they are going to do just fine and go on and mate, spreading the gene further, potentially to an entire population fairly rapidly.
The new technology CRISPR makes it easier to create synthetic genes that selfishly copy themselves within the genome (note: this is definitely not the only application of CRISPR) and could confer positive traits that are helpful to humans, like mosquitoes resistant to being carriers of malaria, or to introduce deleterious mutations into a population.
As you point out, introducing a mutation that causes sterility and having it spread is still not easy. There are a few clever approaches, though, that can make it possible. Note that the strategy does not to have 100% effectiveness to wipe out a population: once below a certain level, members of the population may have trouble finding mates and face greater predation pressures and the population can collapse.
One technique is to boost the proportion of males. If you can force all the offspring of one male to be male, the proportion of males in the next generation will be higher. Those males-that-only-produce-males don't have any immediate reproductive disadvantage versus normal males. If they survive and mate normally, they will continue to compete with normal males (they may also compete with females for food resources during their lifetimes). Any time a normal male mates, sure, it will create a new generation of some females, but every time a transfected male mates it will effectively double the number of transfected males. Even as the total number of individuals in the species drops, the proportion of transfected males remains high. Eventually there are too few normal males to mate, the number of females drop to unsustainable levels, and the population crashes.
This approach is similar to the technique of releasing sterile males which has been used successfully for population control. The difference is that the gene drive technique raises future generations of the (sort-of) sterile males by itself, which might mean it can be used in population control when it is not possible to lab-raise large numbers of sterile males.
Note that use of these technologies is very controversial. There are concerns that such a gene could accidentally move from one species to another, for example. Future use of the technique will require combined research into safety and efficacy.
Burt, A. (2003). Site-specific selfish genes as tools for the control and genetic engineering of natural populations. Proceedings of the Royal Society of London B: Biological Sciences, 270(1518), 921-928.