The OS is extremely relevant when the idea is to take what we know of today as the Steam client and make a "dedicated" consumer device that runs those games. And the reason is because you have N number of games that can run on a Steam + Windows and N/100 games that can run on a Steam + Linux.
So how exactly is the OS then not relevant? It is only irrelevant if the plan is to make a system for which you plan to write all new games, and/or only have the limited number of Linux games available that we have today.
I even develop and debug on both Linux and Windows at work (although by far I prefer to develop on/for Windows).
And this proves what exactly?
That I'm not completely ignorant about Linux. But that thinking it is going to be this wonderful new gaming platform is bound for failure due to the main reason that such a system has no advantages, just disadvantages.