Wow, you totally misread that quote.
You said - “So Prager is telling us that if we don’t believe in God, we don’t believe in anything.”
The actual quote - “When people stop believing in God, they don’t believe in nothing — they believe in anything.”
The quote clearly contradicts what you say.
What Chesterton said, and Prager quoted, was that not believing in God leads to a belief in anything.
The truth is that everyone has some system of beliefs, for religious people it is derived from God, for the non-religious it is based on something else, materialism, utopian philosophy, Communistic theory, the ideals of Nazism, etc.
Well you have me there but can you actually explain the difference between believing in anything and believing in nothing?
Think about it. What could believing in anything actually mean. It has to mean that you have NO core beliefs - you will listen and believe anything you hear. Believing in "anything" and believing in "nothing" are not actually opposites. Believing in "something" is the opposite of believing in "nothing".
In any case, the quote above is just nonsense. If it's not then explain to me what you think it means.