No other cause went up to a meaningful degree in terms of death rates, which is what the submitted article mostly focused on. "The overall rate of deaths from cancer decreased from about 215 per 100,000 people in 1991 to about 169 per 100,000 people in 2011, researchers found." An article in a series on Slate, "Why Are You Not Dead Yet? Life expectancy doubled in past 150 years. Here’s why"[1] Provides some of the background.

Life expectancy at age 40, at age 60, and at even higher ages is still rising throughout the developed countries of the world.[2]

Yes, people all around the world eventually die of something, but they are dying at ever later ages after longer and longer spans of healthy living all around the world. That's why we can say that death rates are going down. As the link you found after your comment edit says, "Although single year improvements in mortality were often small, the age-adjusted risk of dying dropped 60 percent from 1935 to 2010."

After edit: another participant here in another comment links to CDC documents that plainly show the drop in all-cause death rates in the United States.

[1] http://www.slate.com/articles/health_and_science/science_of_...

[2] http://www.nature.com/scientificamerican/journal/v307/n3/box...