Germany's official measure of unemployment is constructed differently than the U.S. measure. They count people working part-time who want full-time jobs as being unemployed. In contrast, these people are counted in the United States as being employed. As a result, the official measure is not directly comparable to the U.S. measure. Fortunately, the OECD constructs a "harmonized" unemployment rate which essentially applies the U.S. methodology to the unemployment measures for other countries.
Since the OECD measure is readily available, it is difficult to see why the NYT used the German official measure in an article on growing poverty and inequality in Germany. The piece tells readers that Germany's unemployment rate is 5.7 percent. This is the official German measure. The unemployment rate using the OECD's harmonized measure is 3.7 percent. Since few readers are likely to be familiar with the methodology used to construct the German measure, using the 5.7 percent figure is misleading to them.