The statement quoted in the question is hedging, a clear sign that its authors are uncertain of the reasons for the gender imbalance at birth. As with anything in the scientific realm, there are usually more variables than can easily be considered or even filtered.
It used to be that about 106 boys were born for every 100 girls. The numbers of boys are in the decline, a sign of loss in fertility. This is most probably a result of environmental toxins, but may involve other lifestyle factors as well.
WebMD has a page HERE that details some of this (and the CDC concurs). As its author points out, new mothers and young fathers tend to conceive more boys than girls--a clear sign that fertility is involved.
One theory, believed by many but still questioned by others, was promoted by Dr. Valerie Grant, Mr. David Rorvik, and Dr. Landrum Shettles (one article HERE). It involves the physiology of sperm. Biologically speaking, because the female X chromosome is very large, relative to the Y chromosome, "female" sperm are also claimed to be somewhat larger. Their advantage is said to be endurance--being likely to survive in the womb longer than the "male" sperm. But they are thought slower at swimming, particularly given certain environments. Younger couples tend to be more active, and are more likely to have coitus near the time of ovulation, giving the advantage to the "male" sperm. There are other factors involved, however, including the levels of acidity in the birth canal, and even how the mother's body protects and nourishes the sperm while waiting for ovulation.
As to why more females are thought to perish mid-pregnancy, the answer may be as boring as that it simply appears to be so because the mortality of boys at both the early stages and the late stages is higher. Could it be, for example, that boys are more prone to getting strangled by the umbilical cord? There are some distinct gender differences with respect to the development of the umbilical cord and placenta, including increased risks for boys in the latter period of gestation, as noted HERE.
Even though more boys are born, boys have a lower survival rate. They can be more accident prone, more likely to succumb to sickness, or to have more impairments from birth defects. By the early teen years, the male-to-female ratio has usually corrected itself, and by the twenties there are more females in the population. One chart providing a quick overview of this information for US populations can be seen HERE.