The article says the reference is somewhere in here, but it does not seem to be: http://lisa.revues.org/802?lang=en#ftn2
His article is really a wide-ranging essay about movie tastes and U.S perceptions around the world. The final sentences read: "The Russians managed to obtain a print of 'Grapes of Wrath' and displayed it widely behind the Iron Curtain, hoping to convey a harsh impression of the United States. But the main impression, reported by our embassies, was 'In America, even the tramps have cars.'"
Sulzberger (part of the family that owned/controls the NYT) was a well-regarded establishment journalist. So we're on pretty safe ground to assume that at least one U.S. diplomat told him what he quoted. But then it gets hazy. Was this just the diplomats' ready-loaded witty retort? Or an overheard murmur from a couple Russians? That'd be my guess. We're way short of knowing what the vast Slavic world deeply felt.
Kind of amazing how that sort of aside comes to be treated as broad-based fact nearly 70 years later.
from https://journals.openedition.org/lisa/802?lang=en which you linked. That quote seems pretty clear.
I think maybe the target ("#ftn2" in http://lisa.revues.org/802?lang=en#ftn2) is confusing.
Without any of that, the story is "The Grapes of Wrath ran for weeks in Soviet cinemas."
And Steinbeck was famous in Russia for releasing his fairly positive "A Russian Journal" around the same time.
It's impossible to know who exactly ordered it, but it is likely Stalin was aware of it being shown.