This was an ideal animated sequence to use because it only has a black background. I opened a gif made from the matrix screensaver (it loops properly). Then I used 'filter all layers' which is part of Gimp-GAP. I used 'color to alpha' from the many plugins in GAP 'filter all layers'. Then just select the background color and it clears it on all layers. You may have to select a couple of other background shades to just get the moving rain fonts. Then you have the 'rain' sequence on a clear background. I made an image of Wilber the same size as the layer sequence with a black background, placed it at the bottom of the layer stack and did Filters > Animation > Combine background. Then deleted the Wilber background from the layer stack. Export as a looped GIF.

That is a general run-down on basic animation in Gimp. I also used G'Mic > Colors > basic adjustments to brighten-up the letters. Many Gimp users don't realise G'Mic works fine nearly all of the time on animations. I've found it's best to use the 'active layer' as the input layer to make adjustments and when happy select 'All' as the input layer. Nearly all G'Mic filters work with animation in this way. Some take time to render...

I use the Gimp 'big 3' for animation which for me is G'mic, Gap and MathMap. I use Xubuntu on a box with the most ram and a version of Gimp that is not under development. I love open source software.