The specs of every card are plainly viewable on nvidias website.

DX11 is backwards compatible with 9.0c, which in some instances, if you can use DX11, it might be a little faster than 9, however, any new visuals or advanced features of DX11 are all GPU hardware based. FFXIV makes use of these hardware features, so if you dont have it, then you cant run it. Now some games will let you select DX11, and in this case, the DX11 is basically running 9.0c with maybe a few software tweaks that may improve performance.

Anybody can have DX11 installed, regardless of their GPU make.