Most Southern States allow one to carry a loaded long gun in their vehicle and open carry of a long gun is legal. You are correct... CCW plays no part of this.
According to wiki...
https://en.wikipedia.org/wiki/Gun_laws_in_Georgia
There are a number of ways a firearm can be carried without a permit.[1][9] No permit is needed:
To carry a firearm in a person's home, place of business, or vehicle
To carry a long gun in a fully open and exposed manner
To carry an unloaded firearm in a case
To carry a firearm in someone else's vehicle, provided you would qualify for a permit
To carry a firearm while fishing or hunting, if you have a valid fishing or hunting license
The fellow did not banish the gun (point at jogger) until attacked as far as we can tell.
The jogger had a hammer (who jogs with a hammer), but unless you are a felon both (shotgun/long rifle) are equally legal to open carry.
I think the word your autocorrect may have been looking for is "brandish".
Something hinky is going on there, one way or the other. Have the break ins stopped? Is there any physical evidence to tie the deceased to the break-ins?
This is the first I have seen about a hammer, but I have known people who routinely carried a hammer, one lady in her purse.