Security Guards Exempt
Well, although the Public Gatherings statute doesn't itself say that it has an exception for armed security guards, the security guard statute DOES. If one law says something is permitted and the other says that it is not, we would normally apply the law that was more recently passed, and conclude that it implicitly repealed the conflicting provisions of the older one. But if there is not a direct conflict, the rule to follow is that the more specific law controls over the generally-worded law.
In this case, the generally worded law is 16-11-127, by saying "don't carry guns at public gatherings."
The more specific law is 43-38-10 (f), which says a properly-licensed guard can carry where others cannot, and is exempt from the following statutes:
(1) Code Section 16-11-126, relating to carrying a concealed weapon;
(2) Code Section 16-11-127, relating to carrying deadly weapons at public gatherings;
(3) Code Section 16-11-128, relating to carrying a pistol without a license; and
(4) Code Section 16-11-129, relating to licenses to carry pistols and revolvers generally.
So I don't think it's valid to say that armed security guards can carry at public gatherings because they have permission from the manager of the property. They carry there by virtue of the legislature writing an exception for them into State law, and linking that exception to a special kind of license not found in 16-11-129.
The thing about gun shows is more on-point. But keep in mind that gun shows have involved people bringing guns to public gatherings for generations, long before the law was changed to incorporate the "tell the manager or security guy and follow his directions" provision. So for most of our lives, people have been carrying at gun shows simply out of universal recognition that the legislators were short-sighted when they wrote the public gatherings law and the law is too broadly-worded to literally be applied everywhere it possibly could.