my computer has the Intel® HD Graphics 4000 graphics card.
Wait a minute.... Is this a Windows 8 system?
I'm suspecting that with the newness of it, it doesn't have the older DirectX 8.1 drivers FFXI needs. Steam may not have included it, or it may not have auto installed properly.
Go here and install Direct X 8.1: http://www.oldversion.com/windows/directx-8-1