To a certain extent, almost all premodern nations were dominated by the military. I large share of budget expenditures in almost every premodern state was directly or indirectly used to finance war. I think what makes Prussia so much a "Military With a Country" is the extent to which the state was able to exert it's power over society. Despite it's poverty and small size, the Prussian bureaucracy and allied aristocracy was consistently able to raise more resources through taxes or an efficient draft than other states. As a result, I'd argue it's not so much that Prussia was unusually militaristic (although it probably was) as it was that the state had an unusually high level of state capacity.

Bureaucracy and Efficiency: An Analysis of Taxation in Early Modern Prussia