Why does Google give you free email when their core business is selling ads? Simple, it keeps you more connected to a space they control, where they can put more ads in front of your eyeballs. They actually have a formula that they use to project how much money they make from you from every minute you spend on the web, regardless of where you're browsing. This is why all of Google's businesses are things that get you to log on.
SteamOS is exactly that for Valve. Valve's core business isn't making games, its selling you content and taking a cut of that sale. They could care less who produced the content or on which platform you're accessing it. They've done really great on the traditional PC platforms, but their defacto standing is under renewed attack on their largest platform, Microsoft Windows--which is competing now with their own integrated storefront--and under attack on your television screen as well--where the Windows Store will soon extend to Xbox One, and all the other competitors have their own storefronts too--including myriad android devices, some of which from heavy hitters like Amazon, Google, and soon-to-be Apple in all likelihood. Without their own contender in the livingroom, they would have no choice to to cede that space to their competitors -- Few competitors offer boxes with enough power to run the content that valve sells and none of them are interested in lettings third-party stores live on their devices, those with powerful enough hardware--Microsoft and Sony--are even less interested. With the PC gaming market being mature, its not going to grow by leaps and bounds -- console gaming, however, is larger today and growing more quickly than PC gaming. Its a move thats necessary for them to grow or even maintain market share, and also to maintain relevance. If they ceded the living room to Microsoft, Sony, and others, the entire steam platform would become increasingly marginalized as PC gaming looses ground to the consoles.
Linux itself is irrelevent -- its a convenient basis for their platform that they can tune to their needs and which is mature. Developing an entirely in-house platform would cost too much money and time. The platform must also be turnkey and tuned for the livingroom. Normal people don't want a computer in the living room, they want an appliance. That's what SteamOS is -- combined with appropriate hardware and the steam controller.
This is what SteamOS and steam boxes provide valve.
For the consumer, SteamOS and SteamBoxes offer that appliance to play their favorite PC content in full fidelity and with their usual PC-gaming friends. They offer a sort of "premium" console that's more powerful in some respects than even current-gen consoles, and one which can theoretically be upgraded with a more-powerful GPU in a couple years. I've valve can succeed in making SteamOS and SteamBoxes console-simple, then their other advantages will be worthwhile to a significant number of people, I predict, though you're probably right that they won't achieve the ubiquity of the XBox One or PS4 (far from it), though they may do better than the Wii U.