The Gallery app automatically groups photos and videos based on faces. If a picture incorrectly gets tagged with a face, you can remove individual face tags from a picture by opening the details view (by swiping up or tapping the "i" button) and tapping the small pencil logo next to the small previews of the detected faces, as you can see in the screenshot below (picture & name blurred for privacy).
If you open the details view of a video with a face, the whole section where the detected faces are supposed to be is simply missing. I know for a fact that the Gallery app has the ability to recognize faces in videos as well as pictures. This is because if you tap the search icon and select a face, the results will include videos of the selected person.
The only way to remove a face from a video currently is to open the Gallery app -> tap the search icon in the upper-right corner -> select a face/person -> tap the three vertical dots in the upper-right corner, and select "Remove from results". From there, you'll be able to remove this person's face tag from any photos or videos you select.
TL;DR—You should be able to directly remove detected faces from videos by opening the details view, just like you can with photos.
On an unrelated note, the ability to manually add faces to pictures and videos would be handy. That is probably a topic for another post, though.
