Less than a decade ago, it seemed self-evident that Russia was reclaiming its rightful place as part of the Western world. Now Russia is increasingly looking East, toward an uneasy alliance with an illiberal and much more powerful China, and—in recognition of the country’s increasingly Muslim makeup—with nations such as Turkey and Iran. But even more pronounced is a sentiment that Russia, so unique in its vastness, must remain a world unto itself, a country that should expect kinship from no one. Some Russian nationalists now herald this Mongol-Turkic state, governed by descendants of Genghis Khan’s oldest son, as the...