Billy Graham's sermon to which you refer was published in the OCT edition of his magazine, Decision. It made the rounds here on FR last week. It was also clearly stated that it was a reprint of a sermon he delivered in 1962 - more than half of BG's lifetime ago. I agree with his message. Deceased radio commentator Paul Harvey drafted an essay back around the middle 1960's which echoed BG's message and has received much attention here on FR.
YouTube - Paul Harvey, ~1965: If I Were the Devil
video run time = 00:03:23 minutes
I have listened to that 1966 broadcast by Harvey before, and I just clicked your link and did so again. He was prophetic.