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.
The T4 programme started in 1940. There were public protests of the T4 programme in 1941. The T4 programme was the mass killing of disabled - mostly learning disabled- people.
The T4 killings are seen as the precursor to the mass extermination of Jews, with refinements of killing methods.
Six different camps were used. People were killed in gas chambers, or by lethal injection, or by starvation.
That's all true, but we're talking specifically about the extermination of Jews. Is there evidence that the Nazis planned T4 as a trial run of Jewish extermination, and if so would NYT have known about those intentions in 1939?
The Dachau concentration camp you mentioned has a gas chamber but it wasn't used if I remember it correctly (was there on a school trip).