What makes Chuck Klosterman's writing believable, or credible in a sense, is his honesty. He is very transparent in his writing; he gives his opinion about anything and everything, no matter how brutal or frank. Even though his pieces are notoriously slanted, Klosterman presents his opinions in a way that helps his readers to understand him as a person and a writer.
Another thing that effectively portray's Klosterman's voice is his attention to detail. Throughout the article, links are posted so the reader can understand exactly what Klosterman is talking about the whole time. Without these links, we would have to take Klosterman's word for it, but with the links, we are able to experience it for ourselves.
Overall, Klosterman's writing appears credible simply because he writes intelligently. You can tell from reading his articles that he is a smart man, and that makes people trust him to a certain extent.