Writing graphics code in a unified model is quite a bit different from the conventional x86 model.

It isn't. The difference is pretty small, and it's just optimizations for when copies can be skipped and not a radical change in the approach of how rendering is done.

Intel would need their own equivalent to Metal if they wanted to do a similar move.

Not at all. If big-ish changes were required, they could be exposed as Vulkan extensions.

I don’t know enough about Vulkan to say if it’s compatible with this kind of approach

Of course Vulkan, the graphics API used on all modern phones except Apple's, supports using integrated graphics efficiently.