They EMail you a Seriel Number that is attached to your Stardock account when you buy the game online. You can then download and install the game many times using the Seriel Number. I am pretty sure there is not a limit on the number of instalations but I'm sure someone will post if there are.
Also the Stardock Gamers Bill of Right States: 7. Gamers shall have the right to re-download the latest versions of the games they own at any time.
So you would think you would be able to after reinstall youre OS.
But again I'm not 100% sure so it would be nice for someone to post a conformation about this.
A full copy of the Bill can be found here: https://forums.sinsofasolarempire.com/?aid=322522