If you have added Quake Live to your hidden category, you need to change to the games category to show games you own but not supported by your OS, then scroll to the hidden category on the larger list.
Quakelive is in neither my games list nor my hidden list. I am fairly sure my hidden list is unfiltered and that I did not put quakelive in my hidden list.
According to this article, Quake Live is no longer free and no longer available for Linux (which I assume also includes SteamOS): http://linux.softpedia.com/blog/former-free-to-play-quake-live-now-9-99-on-steam-linux-support-dropped-495924.shtml
That is what I originally suspected. I contacted quakelive support first and they gave me a steam key but the game still didn't show up in my library. The steam store and steamDB says I own it. It just isn't showing up in my library. I assume i could still run it if I was on another platform by running
steam://run/282440
Closing as resolved back in 2015.
It is not found in my library despite having it before. I talked to quakelive support and they gave me a steam code. I used it, but the game is still nowhere to be found in my library. I looked in the hidden category as well as the games category (where there is no steamOS filter), On the Steam store is says it is in my library.