Nuclear Strategy Is not what Hollywood Depicts it as
In movies you always see these big dramatic shots of missile swarms targeting centers of population. To be sure, that is ONE tactic that can be employed for nuclear bombardment, but its not actually the most likely one. It just shows how we as people vastly overestimate our value to our rulers. We as a populace actually aren't very valuable as strategic targets. I'll explain briefly some nuclear strategic options and deployment then it will make sense why there was "no military presence."
So lets say you have a big land war between two nations, things are going bad for one so they use a nuclear weapon to wipe out a carrier group or a massive tank division or something. Hollywood now has all the silo doors opening and going berserk in a radioactive orgy of cinematic destruction that would make Michael bay weep tears of awestruck wonderment and joy. Not so. The leader of the nation that was just nuked has several options and you can be guaranteed that he will consider them very carefully.
Tit for Tat- Deploy a singe device the same size as the one the enemy used against a military target of equal value to demonstrate that you are not deterred but also aren't looking for an escalation. The hope is to get them scared and bring them to the bargaining table.
Up the Ante- You deploy two devices against military targets of very high value. The idea is that you are telling them you are willing to go all the way on this and hope they get scared and come to the bargaining table.
Hard Strike- You assess that the enemy is willing to go all the way and that anything less than a full preemptive strike against hard military targets will result in your destruction. You target military bases, nuclear launch sites, and centers of government to attempt to destroy the enemy capability to fire more nukes at you. The idea is that you shoot first and destroy all of their military capabilities before they can get their missiles off the ground. Hopefully afterwards they will be willing to surrender or come to the bargaining table.
Soft strike You target cities simply for the pure meanness of it hoping to break their will and ability to support their military and government. This is the typical Hollywood style all out nuclear holocaust you will see in theaters. Its really just a nuclear version of the WW2 terror bombing raid campaigns used by all sides in that conflict. The idea is that industry will be destroyed and the will of the people will be broken. It persisted after WW2 for long enough that it has become the most well known strategy, even though it is outdated and actually the last option on the table out of many many others. As both the Axis and Allies found in WW2, terror bombing doesn't really work. Pearl harbor, and the firestorms in Tokyo and Dresden only seemed to harden the resolve of the respective targets. Whats worse, by using such tactics you open the door to having them used on yourself.
So to answer your question, The nuclear war was one which used the hard strike option. The primary targets were military installations, troop formations, naval fleets, air bases, missile launch sites, and centers of government. That's not to say the populace didn't suffer, they did greatly, but they were merely the collateral damage, not the primary targets. The military is already less than 1% of the populace, very very few units survived, and without effective leadership the few survivors simply deserted. There was no effective government left, people were starving, dying from preventable diseases, no clean water, no food, people were dying from rad sickness and no help came. The secondary effects of a nuclear caused social collapse would actually kill as many or more people than the bombs themselves, and no help came! The military and government became objects of bitter resentment and loathing to the hard-bitten survivors. "where was the military? where were out leaders?" Can quickly turn into "there was no military, there were no leaders." This becomes accepted legend over a few years and by the time the 2nd and 3rd generation of offspring are raised military and government have become a mythological bogey man who promised to protect the people then betrayed them and left them to the wolves.