Google / The Internet is your friend.
Reference article for the robocopy command, which copies file data from one location to another.
learn.microsoft.com
But a simple example would be (using your picture example), from the command prompt (I recommend using an administrator command prompt to help ensure no file access issues):
robocopy "W:\Games Folder" "E:\OLD Games Folder" /E
OR
robocopy "W:\Games Folder" "E:\OLD Games Folder" /mir
NOTE: You do not need to specify file names to copy - just the drive / folder location.
The difference is the first will copy all files and folders from the source even if empty. The second does the same but will purge anything from the location being copied to - so if copying in to a folder with other contents DO NOT use the /mir flag.
If you run in to issues you may need to also use the /zb option (although it should be unlikely) - be sure to exit and shut off any games related software such as Steam / Epic / GOG / Riot / Blizzard / etc store apps. Don't forget some games (e.g. Valorant) use an anti-cheat client which runs as a system application - usually they will be installed to 'C:\Program Files' so shouldn't be impacted, but you can never be sure so stop them also.
NOTE: Advice taken at own risk - robocopy can remove data from locations. Also be sure and do a small syntax test on a test folder area.
You should set up the destination folder first if you need to apply any folder / sharing permissions on it.
Other options:
just do the whole drive to the other:
robocopy W:\ E:\ /mir
Or mix it up with the whole drive to a folder on E:
robocopy W:\ "E:\OLD Stuff" /E