That old copy of the New York Daily Gazette you showed us, the one printed from the library's microfilm... just seeing a newspaper that was published in 1789, that was really cool.

1. That old copy of，那张旧版的...

2. just seeing a newspaper that was published in 1789, that was really cool.

这个句子很简单的。开头是现在分词短语，里面含有一个定语从句。在这里作状语。

that was really cool 是个完整的句子，不是定语从句！that 是指示代词。

刚刚看到一份1789年出版的报纸，那真的很酷。