This makes it sound as though one and the same child has been protected from genetic defects. But of course that's not it at all. Rather, the happy future is lived out by a different child than the one who would have lived without the screening. The damaged potential child is not healed, but replaced. This is arguably still an improvement, but the difference is worth noting.
I guess there is a reading of "their children" where it means something general like "whatever children they end up having", rather than referring to any particular individuals. But it is not the most natural reading. The woman quoted in the main article seems to have a clearer conception: "I truly believe that God gave us this technology to be able to protect our next generation." It's the collective generation that is benefited here, not any individual children.
Also of interest are three quick ethical objections mentioned in the article:
 Some disability advocates say the screening is a form of discrimination and implies that a life with a disability or illness is not worth living.
Indiscriminate judgment is not necessarily a virtue, especially for parents. Anyway, I think to choose a healthy embryo merely implies that disability or illness is a (pro tanto) bad thing -- worse than good health, not necessarily worse than nothing at all. That should be uncontroversial. You know, like why we don't deliberately cripple newborn babies. We recognize that they're better off without it.
 Groups against abortion are opposed to the procedure because it involves the destruction of embryos.
Isn't the destruction part of the usual IVF process, rather than the screening per se?
 Other critics fear that embryo screening is a form of eugenics (selective breeding) and a steppingstone to choosing only those babies who will grow up athletic, beautiful and smart.
I'm not sure what's so bad about choosing to have athletic, beautiful and smart children.