This is for anyone who wants to have random gameplay videos for their Big Box setup. The problem I had was a populated Video Path on my platforms. My Steam platform didn't have a video path specified like all my other platforms did. That's why random videos on Steam worked. I tried deleting the Video path for other platforms directly via Launchbox application settings. I found that can't simply delete it. It will just reappear. So I followed the steps below to achieve my results:
1.) In Launchbox, go to Tools > Manage Platforms. Select a platform you want random gameplay videos for & choose "Edit". If your video path is populated, you'll need to remove it.
2.) To begin removal, navigate to your Launchbox folder on your Windows Explorer. Select Videos > Platforms. Delete the video for the platform(s) you want random videos on Big Box for. This is to ensure Launchbox won't re-populate the Video path after doing step 3.
3.) Go back to the Launchbox application & choose Tools > Manage Platforms again. Select the platform you want random videos for, delete it (unfortunately), & add it again.
4.) Go through the metadata process for that platform to add your games again.
5.) Go to the Big Box menu & select Options > Videos. Make sure "Use Random Game Videos for Missing Platform Videos" is checked (I noticed other people couldn't get that option to work. I believe they had the same problem as I did).
Random videos should now be playable on your preferred platforms following this method. If the devs or anyone else have a much faster way (e.g. XML settings) to accomplish the above, feel free to add it. c: