I don't know all the details of this incident but, according to the article, her first visit to the ER resulted in a diagnosis of strep throat. To my admittedly non-medical experience that wouldn't be considered to be a life threatening issue related to pregnancy which required an abortion to save the woman's life. The second visit, according to the article, found sepsis but, again, that isn't something that, to my admittedly limited knowledge, is related exclusively to pregnancy.
In the article(s) we are not told much of anything about the entirety of the situation but the Texas law is, of course, cited as the cause of everything that went wrong. The Texas law DOES NOT prohibit a physician from performing an abortion if the life of the mother is at risk. Sepsis would present such a risk but, if caught and treated properly, could have saved both mother and child. It certainly appears that there was a professional failing or two along the way when it came to this woman's treatment but I don't see how this was the result of the law.