I have this same exact problem.

I have two laptops that I use to play FF14. One of them I constantly keep updated with windows updates and the other I haven't used windows updates for about 4 months.

Once Dx11 support came out, I downloaded the patch on both my laptops.

The computer than I keep updated consistently gets the 2002 error when trying to use Dx11 but works perfectly fine with Dx9.

The other computer that I rarely keep updated worked just fine in both Dx11 and Dx9... Until recently. Last night I decided to get all the updates from Windows update and suddenly Dx11 doesn't work any more.

Checked to see if I had the latest Direct X and I do have the latest version.

Our problem must lie somewhere within Windows Updates changing some settings which I can't pin point down.