Pretty much that is it.
State apperatus is one hand of the Emperor, army is the other hand. Both are to be loyal to the Emperor. Now just replace emperor with CPC.
In Chinese political philosophy, there are two concepts that are erronously translated to English word state. One is 天下/社稷 which means the whole political structure, the other is 政府 which is the narrow sense of state, better translated to government. The emperor is the representation of the first concept, the government is the narrow sense. Also important to remember is that army has never been a branch of the government, but rather a parallel branch directly under the control of the emperor. This is the same in pre-morden western world as well. The so called "army loyal to the state" is a concept in the west after the Kings lost their political role to the parliment or congress. In constitutional mornach, the parliment is the owner of the state by forcing the King to give up, in a republic like US it is the congress who founded the state through war of independence and owns the state. However in PRC, it is CPC who founded the state instead of some sort of congress, therefor CPC took over the role of emperor, and the army should be loyal only to CPC.
