The underlying premise of your comment is, at very least, debatable. Death camps were in operation far earlier than you imply, if you leave the semantics aside.

Take a look at the report from Dachau in the New Republic (1934) [1], the report by Gerhard Seger from Oranienburg (1934) [2] and contrast those with Hitler's word in his speech from January 1939 [3] or in Mein Kampf from 1925 [4]. There were reports by other people I'm unable to find right now. If you combine the information with an open mind a picture emerges, one that could have possibly found its way into the NYT in 1939.

[1] https://newrepublic.com/article/119850/1934-report-dachau-co... [2] http://library.fes.de/library/netzquelle/rechtsextremismus/p... [3] http://www.yadvashem.org/about_holocaust/documents/part1/doc... [3] https://en.wikipedia.org/wiki/Mein_Kampf#Antisemitism