It doesn't strike me as very plausible that NYT would be reporting on the extermination of Jews in 1939. If they were, I am eager to learn about it. If anyone knows more about this, please link me to it.
To my knowledge, mass exterminations didn't begin until 1941, carried out by gas trucks and firing squads. The Final Solution was formulated in 1942, with the first death camps going into operation that year. In 1939 the Nazis had already started exterminating some "undesirables" (including at least the disabled and mentally ill) and they were already operating concentration camps, but the nominal goal of these camps was the eventual deportation of Jews rather than extermination. I would be surprised to learn that any Allied governments (or those who would become Allies) knew about the extermination of Jews in 1939, let alone the press.