Hello Ben,
For video files with the date in the file name I use a meta data template and change the XMP::photoshop\DateCreated and XMP::xmp\CreateDAte tags. My filenames are YYYY-MM-DD hh-mm-ss and I use below to fill the tags:
{File.Name|substr:0,4}:{File.Name|substr:5,2}:{File.Name|substr:8,2} { File.Name|substr:11,2}:{File.Name|substr:14,2}:{File.Name|substr:17,2}-05:00
with -05:00 as the time zone. That works well for most movies, it will create an xmp sidecar file with the tags.
I had one case where the camera included exif data in the file and exif tool is not going to work with movie files as Mario already mentioned. The solution for me was to add the movie file to an container or encode and compress it with ffmpg. I ended up batch compressing this movie clips with ffmpg as the files got much smaller without visible degradation. That sounds complicated, but it is really fairly easy after doing some research. If you run into this problem, I can post some more information on how to do that.
Heiner