This misses one extremely important thing, in my opinion: the corporations. The State, as it has become in the developed world since the end of WW2, is not only the public/government institutions, but the private ones with which the former are intertwined.
The Corporate State is the synthesis of socialism and capitalism. It allows private ownership of the means of production instead of central planning, but only if it stays under the "guidance" of the ideology that those in the public sector want to impose.
In our most current iteration, the ideology is now generated by both sectors -- they have fully merged to that point.
The banking system is the most glaring example, due to the enormous importance that money has in the deployment of the ideological goals of those in power. But it permeates everything. Nothing escapes from the State.
