Michael, really, I'm not unfamiliar with English language. But let's go over the sentence for you:
These methods do not include theological or religious axioms, such as biblical infallibility.
So the methods do not include theological axioms, neither do they include religious axioms. Now, an axiom is a statement that is taken to be self-evidently true. In case of theological and religious axioms these would be statements like "God exists" or "the bible is infallable". But leaving those out does not mean you leave the bible out. You just do not approach the bible with the mindset that it is a literal truth or that God exists. Nowhere does the statement imply that the bible is not used.
Now take that with the preceding sentence:
"These historical methods use critical analysis of gospel texts as the primary source for the biography of Jesus, along with non-biblical sources to reconstruct the historical context of first-century Judea. "
If you read this sentence, you will notice that it explicitly uses the gospel texts as a primary source. The gospel texts are biblical texts, something I am sure I do not have to tell you. So what the paragraph you quoted tells us, is that the bible, more specifically the gospels, are used as primary texts to establish the historicity of the bible. However, these are approached without assuming (not including) the existence of God or biblical inerrancy. In fact, when you read the rest of the paragraph, it becomes clear that the extrabiblical texts are mostly used to reconstruct the historical context of Judea and there used in establishing the historicity of Jesus is minimal at best.