The game uses more than 2 cores. It's capable of utilizing all cores of an i7 or better (4 physical, 4 hyperthreaded). Anyone who tells you otherwise has no idea wtf they're talking about.
Take a GTX 460 or any mid-high end card and try running FFXIV with a mid-high end dual core CPU and I guarantee you'll hit a bottleneck with the game using up 90%+ of your CPU while only using 40-60% of your GPU (up to 70% GPU usage on higher end dual cores, which is still a bottleneck). You can somewhat alleviate this by raising your graphics settings to put more load onto the GPU and taking some of the workload off your CPU, but it's not a great "fix". It's just masking the problem.
Now put the same GTX 460 or any mid-high end card and run FFXIV with a mid-high end quad or more CPU and you'll notice CPU usage down to 40-60% distributed evenly through all cores while GPU usage sits at around 90%+. This is what you ideally want, as there is no CPU bottleneck and the game is pushing your GPU to its capacity, meaning your GPU is actually doing its job.
So, no, FFXIV isn't limited to 2 cores. Alpha and Beta were limited to 2 cores, but not the version we play now.
And to the poster before me, you're living in the past. GPU's handle multi-processing like that these days with SLI (offloading tasks such as PhysX, Ambient Occlusion, etc. to one GPU while the other focuses on rendering). Even setups with single GPU's barely offload any rendering to the processor anymore. That only occurs when you're running low res and not utilizing the full capabilities of your GPU, which is what happens when you have a CPU bottleneck. That's why you see people with CPU bottlenecks actually get lower performance when they lower their graphics settings instead of raising them (less GPU usage equals more CPU usage).
@OP: I notice you're using a single core CPU. I'm surprised you're able to run this game at all. You definitely want to look into some upgrades. If you don't want to spend much, you can get an AMD X4 Socket 965 with motherboard for under $200 and then just upgrade the RAM accordingly. Though I think it might be time for you to build a brand new rig altogether using the latest tech if you're gonna be upgrading almost every part of your rig anyway.