The improvements that come with DirectX 12 will benefit Intel GPU's as well - especially once you consider the changes with WDDM 2.0, lower memory use, lower CPU utilisation etc.
That depends wholly on Intel...they will be the ones making the d3d12-compliant hardware and writing the D3d12 drivers. So far, in the gpu space, Intel is far behind both AMD and nVidia--(it's been that way for at least two decades.)
You are very correct, most especially, when it comes to gaming the Intel lags behind those two GPU makers.