As the calendar turns toward the final two years of the Obama Presidency, this is a moment to consider the world it has produced. There is no formal Obama Doctrine that serves as the 44th President’s blueprint for America’s engagement with the world. But it is fair to say that Barack Obama brought into office a set of ideas associated with the progressive, or left-leaning, wing of the Democratic foreign-policy establishment.

“Leading from behind” was the phrase coined in 2011 by an Obama foreign-policy adviser to describe...