Does this amphitheater have walls or a roof? If it is completely open air, ask the Law Director why he thinks it is a building.
Even if it is a building, does it meet this definition of "government facility" from ORC 2923.126 (G)(3)(a):
(3) “Government facility of this state or a political subdivision of this state” means any of the following:
(a) A building or part of a building that is owned or leased by the government of this state or a political subdivision of this state and where employees of the government of this state or the political subdivision regularly are present for the purpose of performing their official duties as employees of the state or political subdivision;