In an article on Forbes, Valve confirmed they will end up releasing Steam Machines that are powered by Intel and AMD Radeon graphics.
For the first 300 prototypes, Valve is working closely with NVIDIA on SteamOS. However, they're also working with Intel and AMD too. There will be multiple Steam Machines in 2014 and some of them will be powered by Intel and AMD graphics.
Having a lower-end Steam Machines box powered by an AMD APU would be rather nice from the perspective of cost, power efficiency, and performance. AMD Radeon graphics cards are also obviously nice. What will be interesting though is whether Valve ends up shipping the AMD Catalyst or open-source Radeon Gallium3D driver stack by default.
AMD Catalyst will deliver better performance over the open-source driver, but bugs and other problems tend to be all too common to AMD's binary driver. The open-source drivers meanwhile are only fit if using the R600 Gallium3D driver and enabling Dynamic Power Management. In 2014, the RadeonSI driver should be in good shape and may reach parity to the R600g driver that supports through the Radeon HD 6000 series. At the end of the day though, it's quite likely the Catalyst driver will be deployed due to its faster performance and more advanced OpenGL support.