And no-one has answered my question as to what makes a Linux based "SteamBox" better than say any one of the available pre-built, living-room friendly gaming PCs running Windows and Steam? Hmmm?

One possible advantage: Validation.

With PC games, far too frequently there are quirks to outright show-stopping bugs.  The majority can be minor, but some can be huge - the recent hit Sleeping Dogs for example, takes 15 minutes to start on my PC and many others (according to the huge thread on Square Enix & Steam Forums).  It's been that way for months.  Doesn't affect everyone of course, but that's always the case with an open hardware platform with a massive variety.  The fact it may be a driver or developer problem is irrelevant if it just doesn't work.

So, what Valve could do is basically treat the SteamBox like a console - validating games that will work perfectly, or as close as possible on their restricted set of configurations.  Much like they do now with verifying no/partial/full controller support for Windows games in Big Picture mode, you get a "Works with Steambox!" logo, and Valve validates the games with driver updates, etc.

Now, does that then make a Linux SteamBox viable alternative to Windows gaming?  Hell no, bugs or not you're still looking at ~2% of the gaming coverage of a windows system, and that makes it useless for me and many other PC gamers out of the gate. 

So I'm not sure how fully committed Valve will be to this project, this could a long, multi-year thing where they keep testing the waters.  With the MS store and MS seemingly far more interested in pushing the Xbox brand to Windows users than promoting PC gaming (and this will only get worse with the 720 released next year, and considering it might be X86 based and MS's new direction as a devices company, this might be MS's major push for a closed platform for far more than just videogames), Valve is probably looking far ahead  Steam for Windows sure as hell 'aint going anywhere.