Based on the official website, I can say that the program is compatible with Windows 7. There is nothing mentioned about Windows 8/8.1 or Windows 10 which means that it's unclear if it will work or not.
However, I have tested the version from their official website on Windows 8.1 and Windows 10 (both on 64bit) and it worked normally. You can use it on these versions of Windows.
To migrate the data from old computer/Windows simply export it or use the File > Save as. Choose a directory then attach a USB flash drive and move the data to new computer.
Download latest version: http://www.repairshopdirector.com/rsdirector201.exe