How to review a video fragment in XCOM2
Solution 1:
Sorry, the commander quarters doesn't have any plot videos. Also I don't think you can see them anywhere in the game.
Instead, you can watch an youtube walkthrough campaign.
I would recommend THIS ONE. It's nicely organised by missions so, in order to avoid spoilers, you will have to go through mission by mission and check the current objectives at the beginning of each video in order to determine if that video could contain your missed plot video or not.