It looks like Mary McCormack, who was the Deputy National Security Advisor Kate Harper during the later season's of The West Wing, got a good section of the cast back together to help promote her sister - Bridget Mary McCormack, who’s running for The Supreme Court. I guess in the USA the public votes for who goes on The Supreme Court, I don't think we do that here. Anyway, Bridget Mary McCormack, is running on the nonpartisan ticket (I believe this means that she isn't connected to a party - similar to our Independent candidates.) So the video seems like a chunck of the show - I actually thought it was edited sections from previous episodes but I think it is a totally new thing. It mainly reminds Americans about voting in the nonpartisan section of their ballot, which apparently they often overlook.
Hopefully my American readers or Anna will help confirm or correct the above.