Huh, Xbox One and PS4 are very close architecturally, beyond both being x86 based. Xbox One is closer to a Windows 8 PC on the software side, assuming you have a DX11 based game that runs on WinRT, which could make lazy ports easier. In practice anyone that would benefit from a lazy port is probably an indie developer, and is using Unity, Monogame or another higher level framework (or OpenGL and C++ for a weird minority) and AAA developers can't do lazy ports because the performance just won't be competitive.
PS4 isn't really close to an existing set of APIs, although it's possible that Mantle (AMD's low level graphics API) is the same or very close to the PS4 graphics API. There are low level specifics like unified memory, asynchronous compute, and Xbox One ESRAM that make neither system look like current PCs, although future PCs might adopt them through new API specs or hardware configurations.
Steam Machine fits your description more accurately, but even it's a little weird in that a lot of games don't support Linux.
PS4 isn't really close to an existing set of APIs, although it's possible that Mantle (AMD's low level graphics API) is the same or very close to the PS4 graphics API. There are low level specifics like unified memory, asynchronous compute, and Xbox One ESRAM that make neither system look like current PCs, although future PCs might adopt them through new API specs or hardware configurations.
Steam Machine fits your description more accurately, but even it's a little weird in that a lot of games don't support Linux.