I think they’ve taken something like a Homburg that is too small for him, and pushed out the crown. It’s too tall to be a Derby/Bowler, and doesn’t have enough brim to be Boss-of-the-Plains.
Also, the very flash feather marks it as a casual style – they’re really going for ‘ridiculous’, not for anything conservative.
Once again, it is a Top Hat. It is a very plain traditional top hat. Most people are used to the highly stylized versions, but that’s what a basic felt top hat looks like.
Best guess given the video quality: TriPolar is right. Plain ol’ top hat. Google photos of JFK at his inauguration — he was wearing a top hat of just about the same proportions.
re: the OP — Bowlers, also called derbies, were around for roughly a century, and the styles changed over time.
My favorite was from roughly the 1880s-90s, where the brim is curled up more at the sides than in the front and back, which makes the sides higher. What I mean is, when you set it on a table, the sides of the brim don’t touch the table, only the front and back do.