For most image formats like JPG, Picasa writes user tags you enter in the tag panel (on the right side of the picasa main screen) to the image file.
For most (if not all) video formats, though, Picasa does not write the user tags to the video file, but instead writes the tags to the hidden file .Picasa.ini in the same folder as the video file.
You can look at this file using a text editor and you will see that any image file or video file will be listed along with any edits to the image, including tags.
The .picasa.ini hidden file is where picasa stores all information about the files in that folder. When the edits are "Saved", thay are transferred to the image file if picasa knows how to do that, but picasa does not know how to save tags to a video file, so it leaves the tags in the .picasa.ini file.
I don't know how many videos you have, but one way to get the tags into the video file is using a tool like EXIFTool
https://www.sno.phy.queensu.ca/~phil/exiftool/ to manually write the tags one by one to the video files by reading them from the .ini file then using EXIFTool to write them to the video file metadata.
It might be possible to write a script or program to read the tags from the ini file and write them to the proper video file, but I don't have the ability to do that. Maybe someone in the EXIFTool forum knows of a way to do that.
Sorry,
Earl