In order to get 'Star Wars The Clone Wars: Republic Heroes' to start you need to have games for windows live installed. However, for some reason, when downloading from the official Microsoft website, the setup didn't work. Instead I needed to download the setup off of this site https://community.pcgamingwiki.com/files/file/1012-microsoft-games-for-windows-live/ .

Simply download the setup and run it. after you should be met with a login screen. In order to login you need an Xbox Live account, though you can still create one of these so it shouldn't be an issue.

Once you have downloaded the Games for Windows Live client, simply run the game again and it should run!