I almost missed that yes, it is available on Linux. When did the penguin icon get replaced with "Steam Play" on the Steam site? Are all Steam Play games Linux-compatible?
Steam Play is their one license = all platforms thing.
I think the little Steam icon means SteamOS and therefore Linux.
Yes, and yes.
And to answer the original question, it's been like this for quite long; I'd say at least 3-4 years - that's how long I've been paying actual attention to Steam, and I don't remember ever seeing a different icon for Linux.
And having been on steam since The Bad Old Days of Wine (not all that long ago, really), I can say that we used to have a penguin, and then it got replaced with the steam logo a few months after steamos and the steam machines went on the market.