Galactic Civilizations 2 used Bink 1 ".bik" videos, while GalCiv 3 uses Bink 2. Bink 2 does not have publicly available tools with which to encode ".bk2" videos. I tried to have the XML point to a ".bik" file, but then it gets ignored. I also tried renaming a ".bik" file to ".bk2", but GalCiv 3 still thinks it is a Bink 2 video, which does not end well.

One solution would be to still support Bink 1 videos as I noticed that ".ogg" music files are also supported by GalCiv 3 if the path points to a ".ogg" instead of ".mp3". The other solution would be a specific tool with which to encode Bink 2 videos, if Stardock's License with RAD Game Tools allows this.

I asked RAD Game Tools for advice and this was their response:

I’m sorry, but unlike Bink 1, we do not make the Bink 2 compressor available for non-commercial use.