The history is a bit more complicated than that. Valve themselves never released a “Steam Box” that could run games on Linux. They partnered with a few different companies (Alienware, Gigabyte, etc.), who released co-branded “Steam Machines” which were just those companies’s normal hardware design, but with a common set of specs ideal for running SteamOS. See https://en.wikipedia.org/wiki/Steam_Machine_%28computer%29
You might instead be thinking of the Steam Link, which *was* produced by Valve, and *was* a tiny little brick that let you play games on your TV. But the Link wasn’t running the games itself, it was streaming them from a dedicated PC (which may itself have been a third-party Steam Machine) elsewhere in your home. https://en.wikipedia.org/wiki/Steam_Link
You might instead be thinking of the Steam Link, which *was* produced by Valve, and *was* a tiny little brick that let you play games on your TV. But the Link wasn’t running the games itself, it was streaming them from a dedicated PC (which may itself have been a third-party Steam Machine) elsewhere in your home. https://en.wikipedia.org/wiki/Steam_Link