I'm sure this is common knowledge to many of us, but Linux platforms (including game platforms) are not really all that uncommon. Many posts I'm reading on here--the general tone of the discussion--seems to regard a Linux console as an unusual or extraordinary thing.
OK, we well all know that gaming existed in some form on Linux since the beginning. In fact, I'm a little bit impressed by the number of computer games that have been commercially released for Linux in the past two decades, not to mention games that have been cloned, ported, or otherwise created in open source fashion. We've had commercial video card support for ever, and decent APIs to work with... but what about platforms?
We've had platforms too. In fact, my first Linux console was the GP2X, which I purchased upon release in 2005 (7 years ago!). Granted, it wasn't that great of a platform, but it was something. I played Cave Story on it from start to finish, and it was the best gaming experience I had had since I was an adolescent.
However, if you really want to talk about Linux gaming platforms, look no further than Android. We have scores of Android devices in the wild (probably hundreds by now), and they come with all the hardware and software support you can ask for. In fact, I was a little bit surprised just how many games--most of them commercial--have been written natively for Android, and they're not even all casual. I would take issue with anyone who doesn't consider Android to be one of the main gaming platforms today.
So, a Linux gaming console is really not that crazy of an idea. As other people have pointed out, it really doesn't matter that much what OS your console runs... games are not particularly OS-oriented applications. I'm all for free software--I use the stuff all the time, but I still play games on my PS3. Sure, I can't tinker with my PS3 games much or the platform they run on, but if developing open source games were really my thing, Linux is right here on my PC ready and waiting.