The problem is that the definition of "Crusade" outside a Western Christian context is kind of complicated.
For example, Islam has the "Jihad" concept, that can be similar in certain ways and contexts and completely different in other ways and contexts.
It is broader and narrower at the same time.
The "Crusades" of the Middle Ages were a specific historical phenomenon and that notion just made no sense outside Western Christianity. In Early Modern times, the concept appeared, applied to a different context but arguably still recognizable, in the context of some wars between the Turks and several Catholic powers. It can be usefully expanded to encompass some aspects of the Early Modern european colonial expansion, and is surely relevant when discussing Iberian expansion against Muslims in the Peninsula and in North Africa or beyond.
You can have broadly similar phenomena in Eastern Cristianity. Actually, if using the idea as broadly as I am doing, you can argue that some conflicts in the history of Eastern Christianity IOTL may be labeled "crusades". I doubt that this word adds much to our understanding of those phenomena.