The majority of people do not die as children, but the effect of those who do is disproportionately large on "life expectancy" because it's an average.
Let's say that 23% of children die in their first year (true in Sweden in 1751). Let's say everyone else dies at 80. Life expectancy is 61.6 years.
Now let's say time passes and now 0.2% of children die in their first year (true in Sweden today) and everyone else dies at 80. Life expectancy is now 79.7 years. It jumped over 18 years (30%) with no one living any longer than before. Additionally, the percentage of children dying was never even 1/4 of the total, so the vast majority of people still died from other causes.
The point is that the linked chart represents numeric percentages of people dying, while life expectancy weights younger years much more heavily.
Most of the progress that has been made in life expectancy is from young children, but most of the progress in "what actually kills people" has been for older people.
Switch to the 'global' view, that shows very clearly a massive drop because of pregnancy related problems.
It's by far the largest contributor, about 95% as far as I can tell by looking at a graphic.
I think you saw a red band on the chart, which I am looking at as I type this, and thought that red band referred to "pregnancy, childbirth and other obstetric complications," when it is actually the red band that corresponds to "heart disease, hypertension, and other circulatory system disease." The legend for which disease category is which is helpfully arranged in the same vertical order in which mortality from diseases is cumulatively shown on the chart--that's why I'm sure the broad red band that has declined the most is heart disease rather than complications of pregnancy. (My reality check is that I know the approximate base rate of both causes of death during the time period shown on the chart, which corresponds to my lifetime.)