Nope, I've listened to many Peterson podcasts, I've read his books, and I always quote him at length in my numerous articles on his views. So I'm not putting words in his mouth.
In this article I quote was he says in that podcast about atheism. The problem is just that he's an atheist, according to the standard meaning of that word, but he can't afford to admit it without alienating his alt-right cultists. So he's stuck with having to obfuscate the issues. But no one gets to redefine every word in English, pretending to be a profound genius, without coming across rather like an obfuscating demagogue.
For instance, if God is a state of being rather than an object of belief, and that state is impersonal, didn't supernaturally create the natural universe, doesn't perform miracles, and won't reward its followers in an afterlife, then affirming that state of being is consistent with being an atheist. So Peterson would still be an atheist. He just can't afford to admit what he is, so he hides behind a million equivocations and quibbles.
See the third article below for more on how Peterson ducks the question of God's existence.