That video is 13 years old and Gimp 2.6 Old tutorials can be useful, if you read between the lines and apply to an up-to-date Gimp. For example the commentary
"Now to scrape off the paint" Ok eraser on background --hmm fuzzy select signature -hmm Well, even Gimp 2.6 had a color-to-alpha tool. I think something missing from the video, even with Gimp 2.6 painting in overlay mode was not as shown.
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EDIT: I am wrong, using a Gimp 2.8 and a brush in overlay mode works as in the video. If the object is to remove the white border pixels it is not a good method. I think the Gimp 2.10 equivalent is the brush in Legacy mode and Hard Light (i) mode. You might as well threshold the image.
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The signature was from a scan, and while there might be tweaks required in Gimp for colour / textured paper I might go this way.
1. Not shown in the video which used inch rulers but the scan/image resolution does matter. Use 300 ppi which will fit in better with whatever document application you use.
2. Crop the scan to size
3. (optional) If the scan is a little on the faint side an option is Filters -> Generic -> Erode
4. Colors -> Color-to-Alpha to remove the Background. Nothing else required if BG is white, otherwise pick the color.
5. (optional) Various ways to adjust the image if required. This I change the ink colour blue -> black using the Exposure tool but there are other ways, just experiment.
6. Gimp
Saves in xcf format which keeps layers / guides / selections / all sorts of info.
For your signature file you
export. Both png and tif formats support transparency, Gimp tiff export is now littered with options so I recommend png format.
7. Into LibreOffice (LO), it should be the correct size as original signature, can be scaled in LO if required.
I can just get that into a one minute animation.
https://i.imgur.com/NyZ2NNA.mp4