This has nothing do with Linux except that Linux will be able to take advantage ( at least, more easily ) of games writtin in OpenGL. This makes making Linux and Mac ports of games almost painless compared to having to convert a full DX/D3D game to OpenGL which is almost unheard of by most publishers / developers because it simply isn't worth the time. So going OpenGL naturally opens up a bigger audience. They don't HAVE to limit themselves to Windows only, and this is becoming ever more clear in recent years.
THe PS4 uses OpenGL not DirectX. Again, DirectX/D3D are Microsoft only.
Again, it doesn't have to be exclusive. Them simply wanting a Linux version means they're going to be using OpenGL which opens them up to all sorts of possiblities in terms of being able to run it on just about anything with little extra headroom. It's not tied to the fate of their steam machines, as SteamOS is indepedent of the machines, and is run as much by the community as it is Valve.
Another big thing that stopped games on Linux was simply due to complications from buying games. You used to have to buy a game specifically for an OS and it wouldn't run on another OS. With Steam now already on Linux and Mac and shared licenses between all OS's, this makes distribution all that much easier. Let alone games weren't made for Linux before as much simply because of it's open source nature and general opposition to proprietary software and DRM. But now we have Steam ( as DRM system, along with distribution system ) remedies some fears of releasing on Linux, along with the overall change in times in that when I first started using Linux, it was nothing but command line, and today... it's not any harder than Windows, and the command line can be completely ignored just like Windows. Along with graphical package repositories from which every smartphone OS as late ( Android, iOS and even Windows Phone / RT ) took it's cue from, makes it that much easier and familiar.
Doubt Linux and Mac all you want but the fact of the matter is Linux has gained over 400 games in the last 2 years due to Steam pushing for it. Along with big publishers promising Linux games in the coming years. And whether or not you want to admit or not, there is a change coming.
And again, this has little to do with Linux except that Linux will benefit from the shift, and honestly, everyone will benefit from the use of OpenGL. And I'm not saying Linux is going to overtake Windows at all, I'm saying OpenGL is going to overtake DirectX/D3D once again.