Did this newspaper prematurely declare the new president of the United States?

Yes, it did:

The circumstances are similar to the famous Chicago Daily Tribune blunder in the Dewey-Truman presidential contest:

This time around, the issue is not that the media had called the election before all the votes were tallied, but that a call was made long before a number of polling stations in the U.S. had even closed! As an explanation for the German paper's blunder, perhaps it was assumed that the American people were too committed to the socio-political agenda associated with Hillary to not cast their vote for Hillary. Clearly, that was not the case.