Copy all the new BK2 files once extracted from each zip file into the respective folder as per following examples:

(obviously rename / and or move the original files if you want to keep them without redownloading from your game store of choice)

PATHTOGAME/AliensDarkDescent/ASF/Content/Movies/Missions/Prologue
PATHTOGAME/AliensDarkDescent/ASF/Content/Movies/Missions/BerkeleysDock
etc

Replace the files if you haven't renamed / moved the originals

That's it - movies should play in game

Note: The game seems to put a subtitle overlay block in the bottom middle of the screen - this is not in the videos themselves. Possibly disabling subtitles in game audio may remove this.