Yes, it should be the same version of Windows. I'm not sure if it matters if it's 32 or 64 bit or not in this case.

Make sure you are in the right section of the registry. Right click on the word Folder (in the left pane), then click on Export. Name the file and choose where it should be saved.

Copy that file to your other computer, and then just double click it. You will likely get warned about whether you really want to do this.

If you want to be a bit safer, you could export the Folder section on the computer that isn't working so you have a backup.