From looking at your Log.txt file, it appears that you do indeed have an Intel HD Graphics 2000 GPU processor, which is not a dedicated graphics card, but part of the CPU die itself.
The Intel i7 2600 3.4 GHz CPU is a 2nd generation 'Sandy Bridge' variant, which was first introduced to the market in 2011.
If you take a look at the requirements for X-Plane 11 https://www.x-plane.com/kb/x-plane-11-system-requirements/
then you will see that the minimum VRAM is stated at 1GB, which is borderline in your case.
Another requirement is that the GPU should be DirectX 11 capable, which unfortunately yours isn't @ only 10.1 capability.
On top of that, the Log file suggests that the amount of physical RAM that you have is only 8GB, which whilst doable, is again borderline.
Lastly, if High Dynamic Ranging (HDR) is not supported, then this won't help you get the best out of X-Plane 11 either.
With all of the above in mind, you may wish to consider an upgrade?
Hope this helps?