Can I play a game from Steam on different operating systems? [duplicate]
First, not all the games that are on Steam are available for Windows, Linux and Mac, so you need to carefully read the Steam page of the game to be sure.
But if it's a game compatible with both OSes like Middle Earth : Shadow of Mordor, then you can buy it once, and as long as you use the same Steam account on both Windows and Linux, your Steam Library will be the same, so you will be able to install and play the game on both OSes.