If running the very latest Linux Steam client and launching it with steam -steamos there's a few subtle changes beginning to appear within the Big Picture Mode. If navigating to the system area of Steam's full-screen UI, there's now a "SteamOS Version" displayed along with a "Check for SteamOS updates" button. In the strings to the steamclient.so file is confirmation that it's for "[forcing] Steam to believe it is running under SteamOS."
The only other SteamOS-related strings present in the binaries I checked out were about SteamOS updates, a steamos-update binary, and calls concerning under-scan and brightness levels.
That's what appears so far, but we're still digging deeper and will be monitoring forthcoming client updates.