MOSCOW—Russia’s elites think of themselves as heirs to the Soviet Union’s imperial glory. Problem is, they only possess the resources of a second-tier power.

This fundamental conflict between aspirations and means—and between how Russia views itself and how it’s perceived by others—shapes President Vladimir Putin’s high-risk strategy in international affairs, from the Ukraine invasion to the Syria intervention to election interference in the U.S. to more recent forays in Venezuela and Africa.

“Russia...