Islamic State has lost most of the territory it once held in Syria and Iraq. It is vying for survival with other, sometimes stronger, extremist groups. But one sphere where Islamic State still reigns supreme among terrorists is in cyberspace.

The group’s vast online presence is a critical recruitment and marketing tool that has helped it build a brutish brand using propaganda and sometimes false claims. Maintaining the perception that Islamic State can shape the actions of loyalists has become all the more important as its...