The benchmark program is very bad example, but your video card is pretty old, its 3-4 years old in technology.
HD5970 Single Card:
On 1920x1080, I score 3800, and 1280x720 I score about 7000, but in the open beta, I did get some laggy spots even with those higher scores.
I would say try the game and if you experience bad lag, order a new video card, and if your PC cant handle a newer video card then you are where I was before this and had to buy a new PC just to support the new video card.
My old PC with Q6600, 8800GTS 512MB, running Closed Beta, lagged very badly, and my motherboard would not support a better video card, so had to upgrade. Well Open beta was better on my old PC, but I still upgraded, as lag will make or break a game.
Anyways welcome to the forums and Goodluck in your XIV ventures