To put it in terms that are simple and conclusive.
The Error and What it Means
The description of this error by the devs is the following:
"Forza Motorsport 6: Apex has detected an unsupported graphics processing unit (GPU). A GPU with tiled Resources Tier 1 is required to run this game. Some older cards may support DirectX 12 but not the features required to run this title."
Will it Run a Lower Version of DirectX?
Forza: Apex
only runs on DX12 with the Windows 10 anniversary edition update. It is meant to show off their new game engine and DX12. (see images for detailed explanation.)
Which Intel Integrated G.P.U.'s Support DX12 Level 11?
Using this image we can conclude you need a Haswell, Broadwell, Skylake or Kabylake Processor.
Graphics Options
After going through the Video options of the game the lowest resolution available is 720p. There is no further option for render scaling and as far as I remember intel GPUs do not have a scaling option in their control panel.
Since this is a windows store app, you will not be able to manually configure it to another resolution.
Conclusion
Anything less than a Haswell, Broadwell, Skylake or Kablylake CPU will not be able to use the game engine
There is NO way around this!. Even if you have one of the aforementioned CPUs you will most likely get 15 frames/s or less.
NOTE: Please keep in mind that it is likely they have not included all the features required by their game engine.
On Request I could test this game using my skylake if you want me to. (see sig. for model) Let me know