The company they need to beat is AMD. AMD's integrated GPU's are thoroughly trouncing Intel's and are good enough for light gaming. Their weak integrated graphics hurt their core business of CPU sales.
They certainly want to compete in the discrete GPU space, but I think they should be much more scared of losing CPU market share.
Intel integrated GPUs have no place at all in deep learning. They are perfectly good for emulating the 2001 Gamecube and playing classics like Doom and Quake, but they have a bad enough reputation among gamers that if and when they do come out with a discrete card they will have to brand it something other than Intel.