Yeah, for some reason the wrapper GOG uses fo rthis game has issues when switching/showing in-game engine generated screens and then playing the bink videos when they are called on. Anyway you don't need to go to youtube to watch them, you can view them yourself from your PC.
Just go to where you have installed your GOG games and follow this path: GOG games\Star Trek SFC3\Assets\Cinema (yours probably is diffeerent than mine) or simply go to GOG Galaxy, select Starfleet command, and right next to play to the right, you have the sub menu, click on it and select Manage Installation and select show folder. From there, navigate to Assets and select Cinema. You should be able to see all the FMV the game comes with. Its on Bink Video format though so you won't be able to open it with windows media player, so I recommend you to download VCL Media Player (don't worry it's free and its not shaddy at all so you won't catch any surprises, also its waaaaaay better than most media players out there and even allows you to play a little bit with the settings of the video).
Enjoy.
Post edited September 18, 2021 by ReaverT