This gets very complicated in a hurry, and cannot be easily determined because information is missing.
1) Did the off duty cop/security man identify himself as a police officer?
2) Did he have probable cause to chase after the running man?
3) And, as an oddity in Missouri law, did the shooting happen within a two block radius of his duty area?
All of this will have to come out at trial. Unlike an on duty cop, he cannot just be cleared by an internal investigation by his department. Likely the investigation will have to be turned over to another police department, Sheriff’s office, or even the state police.
Whatever....This off duty cop did society a favor.