If you are interested in reading more, you might read Tyler Cowen's Public Goods & Market Failures, which is a collection of articles on the private provision of public goods, and questioning the theory of market failure. Cowen is the General Director of the Mercatus Center at George Mason University - a market-focused think tank. For a more liberal perspective (but the same definition of the term,) you might read Public Goods: Theories and Evidence, a textbook by Raymond Batina of Washington State.
The good in "public good" must be in the public domain not the private, or alternatively of the public as a whole, the definition that the test says is correct fails to include that restriction.