The game currently has an opt-in beta in Steam for owners, since it's not ready yet it's not advertised on Steam directly. The developer recently gave an update on their progress with the Linux version:
Short Update for the Linux Version:
I'm currently working on a new Patch for the Windows version and was compiling a new Linux build last week as I discovered a game breaking engine bug within Unreal Engine 4.
This bug actually prevents certain key inputs to be recognized with the control setup used in Beyond Enemy Lines. So you can't play Beyond Enemy Lines while it's compiled for Linux. Windows Version works just fine.
I now need to wait for an Engine update by Epic. Once confirmed that the new build is working - you should get a full working Linux build (with DLC and Editor Support) shortly after.
It's sad that this is a repeating issue with Unreal Engine 4, hopefully it won't take too long to get sorted. The game actually sounds quite interesting, so I've held off picking it up while it's in a quite beta in the hopes of it becoming officially supported.