For someone to die from a gunshot a bullet must be discharged and strike the person in a vital area.
In this case as in most the gun must be pointed in the direction of the victim (barring ricochets), it must have a live round, and the round must be triggered. If the weapon is in good working order the firing pin must strike the primer when trigger releases the hammer.
Standard gun safety is to never point the weapon at anyone or thing you don't intend to shoot.
To know if the gun is loaded or not
To know if there is a round in the chamber that can be fired.
The shot they were taking that day was of Baldwin pointing the gun in the direction of the camera. That was what their job was that day, so the first control against accidental discharge is basically out the window.
This isn't some crazy shot. It's been done many times before:
Goto 3:45 in this clip from Die Hard and the revolver is pointed directly at the camera
So you have to rely on the armorer to make sure the weapon is functioning correctly and not loaded with a live round.
The first and biggest error that day is a live round made it on set.
The second was that a live round was loaded into that gun
The third was it was not correctly verified to be a "cold gun"
The fourth was Baldwin was told it was cold gun.
The fifth was he was told by an associate producer and not the armorer
The sixth was the gun discharged either through a pull of the trigger, cocking the weapon with his finger on the trigger, or some unknown failure of the gun.
The fact that they let the producer have a plea deal and are going after Baldwin for significant time in jail suggests there's political motivation.