Why treaty cruisers were defined by more than guns

Were these ships considered cruisers because of displacement rather than their gun size?

Yes; treaty definitions used tonnage and caliber limits, so a cruiser did not need a stereotypical cruiser gun battery.

A cruiser could carry four-inch guns and remain a cruiser if its tonnage placed it in that category. The treaty set an upper caliber boundary rather than requiring every cruiser to mount guns near that limit. A battery smaller than 6.1 inches did not turn the hull into a destroyer. Formal displacement and caliber definitions matter more than later assumptions about typical armament.