In other words, his "proof" is a moral argument (ethos) and not logic (logos). "For things to be just, God must exist." or "Morals must be absolute and God is that absolute."
There is strong version of the moral argument most people aren't ware of.
True guidance is God's guidance.
True guidance exists.
Therefore God exists.
Another way to phrase it is, morality is a true guidance to love, the only way for true guidance to exist is through God. Morality in an objective sense exists. Therefore God exists.
There is an elaboration and proof to those two premises and how we can know it.
But as intuitive as the moral argument is, it's my least favorite.