If you happened to be listening carefully, Donald Trump told us something important a few days ago about the profoundly different approach he intends to take toward the Middle East and the threat of Islamic extremism.

The president-elect’s message was largely overlooked because it came in the middle of a typically raucous and rambling “thank you” rally in Cincinnati. News reports focused on his announcement that he would nominate as secretary of defense Gen. James Mattis—“Mad Dog Mattis” as he seems destined to be called by...