Hm...I have an Alienware M11x (not revision 2), and I can tell you FFXIV will let me log in, but crashes with the DirectX device error after the client itself starts up if the Intel GPU is the active video card. It doesn't have features FFXIV needs to render the game. So that's why that is happening.

As to how to actually fix your problem, on my system there is a function key (F6 for me) that says 'BINARY GFX' on it which one must press while holding the 'fn' key to switch graphics cards. It may be a different key for you. It may not even have a manual switch since it has NVIDIA Optimus. I'm not sure if that does automatic switching or just lets you switch without closing all GPU-accelerated applications (I have to close my web browser and/or game to switch, for example, you may not have to do that).

I wouldn't recommend updating your drivers for that unless your system tells you to. The dual-GPU setup on some Alienware laptops is very custom stuff as far as I know. I messed up my system once by installing the regular drivers for the NVIDIA GPU that the M11x uses.

tl;dr : Hit the 'BINARY GFX' key while holding 'fn'.