For a pre capitalist imperial project to exist you need a class/category of people, who are usual self conscious, who dominate a military hierarchy by using military power to extract value from a subaltern people or regions toward an imperial core. The system is circular in that the military hierarchy exists to extract the value upon which its existence is predicated. Also important is that the system is more or less depersonalized, bureaucratized, and expansionary. The ancient Greek west Asian empires are a perfect example of this where you even had ethnic divisions between the military class and the subordinate producing class. You really don’t see this in the crusader states. These were feudal states with very little burecratc control which were dominated by customary reciprocal laws, duties, and obligations. While they were hierarchical between the productive and ruling class, there was amuch more limited differentiation within the ruling class, and a limited drive toward expansion. Additionally there was not an extraction toward an imperial core, taxes and. Appropriation remained local to serve the sustenance of the local nobility. Also interestingly the local Francis nobility quickly developed their own synthetic culture with their Muslim neighbors and would often ally with them against newcoming Christian crusaders from the west. So no the crusades to the levant were not really imperial projects. You could argue more strongly for the Baltic or Hispanic crusades, but even then I think the argument is weak for it. This matters because sloppy historical analysis can throw doubt on the entire project of leftist historiography this strength should be consistency and impersonal rigor as compared to a more personality focused liberal project.