The article quotes the book; it does not say Bannon said those things.
Bannon is the executive director of Breitbart. He wouldn’t feature an article that quotes him if the quotes were false. That would be using his site to spread lies about himself and also to smear Trump’s family. Bannon wouldn’t do that—not unless the quotes are actually true, and he wants to give them greater exposure.
The alternative would be to write an article for Breitbart condemning the quotes as false. But you won’t see that happen. Bannon has already given Wolfe his imprimatur.