Intel has zero marketshare for good GPUs and the worst possible reputation among gamers. The only reason Intel has the share they do in GPUs is obviously because they force people to buy them.
As most pc gamers, you forget to look at it from a different perspective.
Office appliances have zero need for a gaming gpu.
Think administration and anything else that does not need serious 3d acceleration.
Also, Intel provides a complete solution system integrators like for example Dell and HP enjoy.
As a company buys several pc systems at once from for example Dell, they want support and a reliable device. Not an overclocked gaming device.
AMD is trying to get a foot hold for a long time and i hope they will now with zen.
A low power APU SOC would be great to compete for office appliances.
When gpgpu computation power is needed, cuda nvidia cards are separately available and to some extent amd opencl cards(Only because cuda has a larger adoption rate).
Of course, Dell also has some gaming pc systems but it is not their primary market.