ghosterl: Her Story's videos use the FFMPEG 4 (aka FMP4) codec. To see if you can play the videos you can find them in your "Her Story" Folder - on Windows it usually is \GOG Games\Her Story\HerStory_Data\StreamingAssets on your drive of choice (default would be C:).
Pick the one called D101.avi as it doesn't spoil anything, it is just her asking for a cup of coffee (it's also the first video, obviously), although unlikely to be the first you would watch anyway.
If you can't play the video you can try to get the latest codec release from
https://www.ffmpeg.org/download.html - although I didn't need it. I also have VLC -
http://www.videolan.org/vlc/ - installed with which I can play the videos without hitch, albeit without subtitles, I suppose those are hardcoded into the game.
Also, the vidoes themselves do not have the interlacing and glare present when you turn the in-game option "Anti-Glare Filter" off (click on the little toolbox next to the search bar to find the options to turn off the subtitles and the "filter"). So try to play the vidoes WITHOUT subtitles but WITH the anti-glare filter turned on to see if any of those two cause the problems.
Hope that helps, it really is an interesting game.:)
I can watch the videos in the game folder with VLC, but they still won't play in-game... I was wondering whether this was a codec issue myself, I'll try downloading the latest codec release from ffmpeg, though I kind of doubt it'll help, since both VLC and Media Player Classic -- which I have installed -- both come with a comprehensive and extensive list of video codecs that should cover the needs to play the in-game videos in Her Story. I'll also try turning subtitles off and keep the glare on, I must admit I didn't try meddling with in-game options, aside from resolution.
Thanks for all your help, I'm really looking forward to experiencing this game.