I should add, the officer put his own life at risk by not following procedure. If this was the real robber and he had a gun on him, there is fairly good chance he could have taken out the officer. The officer failed to protect himself with cover throughout the encounter. There is a reason is a reason for the procedure. It protects BOTH the officer and the suspect. I believe the negligence in this instance rises to the level of manslaughter.
Until the proper evidence etc comes to light and official action (or not) on this, e.g. court cases. What I'm about to say is just CONJECTURE!
Unfortunately the police officer(s), may have tried to do 2 things at the same time. Check out the faulty rear lights (cracked ?) and/or investigate their suspicions because at some point, before or during the stop, at least one of the policemen noticed a similarity with the armed robber suspect (and driver (and maybe passenger) ).
As you just said in your posts, he should have followed procedure, which early indications are that he DIDN'T.
So the police officer, might have asked for the ID (as part of the "cracked" rear light issue), then while potentially genuinely trying to reach for his ID, the police officer reacts to the gun and/or mention of the gun (concealed permit etc).
Panicking, and shooting the victim/suspect.
tl;dr
This may have been a terrible mess up, and as you suspect, procedures may not have been followed correctly.
I'm disappointed that the police officer was NOT wearing a body camera. Given the significant unrest round the country (e.g. 5 police officers getting gunned down + more injured).
In this day and age, the video evidence would have helped quickly resolve what happened one way or the other.
If the police officer was innocent, they could have released extracts of the video, to reassure the general public, that what happened was unavoidable and NOT because of any fault of the police.