Yeah, that's not something RL could really support since it is only run when a game is launched from the frontend and has no idea when the frontend closes. It should be handled by the frontend natively, or in the case of developmentally dead HS, an app/script on startup or shutdown.
Since nothing has changed with HS and probably not the randomizer app either I would try a reinstall of the app and make sure the video directory isn't read only since the app likely just picks a random video and copies/renames it. Otherwise you would be better off posting on HS and specifically the thread for the app.
If all else fails you could write a script to do it since it's pretty trivial. I wrote one back in the day when I was still using HS.