The cutscenes before and after Missions 2, 3, 7, and 9 are FMVs a.k.a. Full Motion Videos, which basically means they're pre-rendered videos not made in the game engine, and my capture card handles them weirdly when they play. This is why my video will disconnect and reconnect when I skip these cutscenes. Sometimes there will give a bright flash for a second while it's adjusting again, so there's your warning on that. All other cutscenes but those work completely fine though with my capture card because they are made in game, so no need to worry there.

Also while my Elgato is reconnecting I have to play for a few seconds completely blind, but I know what to do so it's k.