1) Unpack the .zip archive with Guilty Force on your Linux somewhere;
2) Find GuiltyForce.x86_64 file;
3) Click on its properties and make sure that you can run the x86_64 file as an executable;
4) Run this file as an executable, for example with a command like ./"GuiltyForce.x86_64"
5) Enjoy! (64-bit version of Linux is mandatory)