I don't know who serious Dave and Josh were when they first started the series but their story is that they wanted to talk about the West Wing as a media phenomenon that was taken to heart by young adults who went on to be a part of US politics and how this fictional media may have influenced those real world political creatures.

What they quickly realized is that the writing of Sorkin was kinda fucked. The stories were fucked, the dialog was fucked, etc. And then realizing that "holy shit, real world politicians were influence to go into politics because of this show" and seeing how real world people in positions of authority are doing "West Wing" logic on the stage of US politics.

As the series goes on, they spend less and less time talking about the actual show and just have a guest on to talk about a few points from the show and then talk about absolutely anything else.