As it was the case with Civilization V, the Civilization: Beyond Earth was also planned for the release on both Mac and GNU/Linux. While the Mac version arrived late, it would seem that GNU/Linux is one that has problems.
Studio Aspyr Media was already in charge of moving the Civilization V to GNU/Linux and therefore they are the same ones that have been chosen to do the same with Civilization: Beyond Earth.
Unfortunately, they seem to face a big problem. While Civilization V was running on DirectX 9 and 11, Civilization: Beyond Earth is exclusively DirectX 11, which causes problems for some graphics drivers under GNU/Linux.
While NVIDIA drivers do not pose a problem, AMD ones do not allow the game to run and it appears that Intel is the source of malfunctions. The only possible solution for now is to remove compatibility with AMD and Intel GPUs.
Currently, there is no fix and this is one of the limitations for the game under GNU/Linux. If correct drivers are not available, the game will simply not run.
Source:
Le Comptoir du Hardware.