... when configured to boot straight into Steam Big Picture mode, the influence of the underlying OS is visible only in the larger game library.
... and the considerable additional maintenance requirements that go along with a full fledged operating system. Considering that Windows has required more frequent patches for security issues than Linux for the past few years, that's not a trivial distinction.
With Windows on it, this little machine can fulfill most of my needs for the living room / home and offers me a platform that i am already familiar with to play my games, (Steam supported or not), get some work done (Office etc) and watch movies.
While this is a valid point, it is a realization of this change in paradigm. With Windows 8.1, it is a regular desktop computer, not a gaming console. While that gives you the ability to do office work and more, it takes it out of the single-purpose, dedicated function, "appliance" category that consoles usually fall in.
With Linux running as essentially an embedded OS, it's likely that updates would be less frequent, smaller, and less crucial to it's overall suitability if skipped. As an example, how long has it been since you've updated your smart TV or DVR as opposed to your desktop or laptop?