You don't even need the external tool, you can use the Steam terminal itself to download the depots, which I personally find more palatable than having another application that is getting access to my username and password (it needs those to get the access from Steam). Even though I don't think that tool is malicious I would still prefer to not have to rely on it.

• Go to SteamDB, and search up your game.
• Click on the app ID of the game you're looking for to go to its details page.
• Take a look at the depots, and click on the depot ID of the one that looks like the one you want to download.
• Click on the Manifests tab. Look at the list and find the version that you want to download. Record its manifest ID.
• Open the Steam console. You can do this by opening a command window "Run" by pressing «Win + R» and then enter the command: steam://open/console, and then press Enter, or by opening any browser and enter the URL-address field write the same command: steam://open/console. You can even have it always available when you start Steam by appending -console to the launch options of the shortcut to the Steam exe.
• The syntax to the "download_depot" command is as follows:
  download_depot [] [] [] : download a single depot
  You only need to worry about the first three arguments to it. Type the command, then the app ID, depot ID, and the manifest ID of the depot version you want.
• Wait for Steam to download the depot. You won't see any indication of progress, but you can tell it's downloading by looking at the network usage on your downloads page. The download can pause/resume if your connection goes out, but won't if you restart the client.
• After the download is done, Steam will show you where the files were downloaded to.
• Go to the game's installation directory, and move the files somewhere else. Then go to where the depot files were downloaded to, and move everything over to the game folder.
• You may have to rename the game's EXE file if the dev changed the launch options recently. You can find the current EXE name by going to the game's SteamDB page and clicking on the Configuration tab. 11. You should now be able to launch the old version through Steam.

Personally I found that you can just start the game from the download location and it will still have the Steam overlay if the game basically uses Steam as DRM.