If you prefer a free editor, Blender could achieve something like this. You need to look at the luma key nodes.
Blender is free but has a steep learning curve. Adobe Premiere could do this quickly using a track matte, but it's not free.
After Effects is also paid-software, and has a steeper learning curve than Premiere, but can also use track mattes - see ...
This would be easy to do with After-Effects. Do the following:
Create a new composition with the settings of the mp4. You can drag it on the composition symbol to automatically create it.
Then, drag your alpha-mp4 above the color-mp4. Now, set the "track matte" to "Luma-Mask" from the alpha-mp4. This should be all.