Manually copying all your assets to your new folder won't work (well it might but it shouldn't)
You need to go to the file menu and select "Export Gathered Project".
This will prompt you to create a new folder which in turn will have a Project_Assets containing all you assets.
Most importantly this will rewrite all the paths within the Terragen project file to point to the local Project_Assets folder.
You can now copy the entire gathered project to any location on any computer and it will open correctly.