Look at the preceding sentence: “Now another interesting thing about the Nightcap Oak is that it is … it represents … uh … a very old type … uh … kind of tree that grew a hundred million years ago. Um, we found fossils that old that bear remarkable resemblance to the tree. So, it’s a primitive tree.” The first 'that' is a demonstrative adjective. The phrase 'that old' refers back to 'a hundred million years ago' in the previous sentence. The second 'that' is a relative pronoun.

The first that is referencing something previously said, while the second that is a conjunction.