Here is the part of /opt/retropie/supplementary/runcommand/runcommand.sh that displays the launching image using either feh or fbi. If you're good with scripting, maybe you could jigger it to play a video with vlc or omxplayer, instead:

You can see where it shows the paths and filename-patterns to look for art, (near the top) and where it defines the accepted extensions (for ext in jpg png; do). You'd want to change this part to include mp4, or whatever format your videos will be in, and possibly also add paths above to include ${ROM_BN}-video or similar if that's how you'll name them.

Then there's the part where the image is displayed with the feh or fbi commands. You'll need to craft a command with the proper options to show your brief video snap, probably with either vlc or omxplayer. Probably also a check on which extension is used to determine whether to use the video or image command, unless you're going to only have videos, and then you'll need to remove the parts referencing images at all, including the "ports" and system-wide launch images (or change them to use the videos too.)

Add splashscreen on Shutdown on Retropie 4.6