It is kind of unclear if they mean carrying a gun or shooting a gun. It says
"The Folling Activities Are Prohibited On This Site:"
Firearms or Hunting.
The only "activity" I know to do with a gun is shoot it.
It also says "Smoking Inside of Park Buildings"
Does this mean you can't even carry in your unused pack of Marlboro's?
You could plead ignorence if called on this one.
Besides it also says "No Violation of any Local, State or Federal Law or Regulation" which you would not be breaking any of. The only ones being broken are by their sign if it is really public property.