Not sure if you've fixed this or not... but I have a suggestion.
Those Silent Oath game segments are actually video files that are played.
If you check out the DX folder, look for files that contain the word "DOT" in them, those are the Silent Oath game videos. Believe it or not, the NGS file is actually just an MPEG file. If you rename the NGS files to MPEG you can play those video files in Windows Media Player.
Now, here's the thing... If Windows Media Player CANNOT play those files, then you're missing the video codec that plays those files. That may be why you cannot progress as the game is waiting for that "video" to end it's playback.
Try downloading the CCCP pack (Combined Community Codec Project) and try again:
CCCP - Combined Community Codec Pack