Indeed. I don't even know if the story is true or fabricated. Still, it's a good discussion.
You missed this part, " (I) Persons possessing a handgun, who are authorized to carry the handgun pursuant to § 39-17-1351..." So, if he has a license then it's legal for him to carry in a recreational park.
However, the law is long and convoluted and is never that simple. There are many "pursuant to (insert paragraph number or letter or another code)" phrases in that law. There are lots of ways for a community to make what he did illegal. But, as you say, we don't know all the information relative to this action.