For some reason you want to change the directory of your artworks (media) and modify your gamelists accordingly.
Here's how:
Close ARRM
Move existing media to new folders
Launch ARRM
Check in the tab Main Options , the checkbox Check if artworks exists (this allows you to reset old links to media that no longer exist)
Load a system
Save gamelist
Close the system by clicking on the None button or by unchecking the system
Check in the tab General options , the checkbox Find missing images