Others have mentioned software that can up-res while resizing, but unless you're using IMAX's top-secret DRM software (how they get 35mm film blown up to IMAX film), you're really not going to have a lot of luck with this image.
Here is what I recommend. I'm *guessing* it's Final Fantasy, but I don't know any of that stuff. The shot is either a screen shot or a composited image made by someone for some specific purpose. I would keep looking on Google Image search as well as on FF message boards for a larger image.
I've been in the same exact boat as you, but I will search every possible keyword until I find what I'm looking for. (Otherwise I just change my mind on what I want for wallpaper lol.)
Once you find a high-res, larger image, then you can re-size that one to your wallpaper size if you need to.
Edit: I thought I'd give it a whirl really quickly. The original image is a composite of several images. I took the image you posted and separated it into four parts: two faces, hair, and the blue lantern. I enlarged them at different rates and used unsharping masks to enhance sharpening. See the link below for a 1680x1050 wallpaper. It's not exactly the same, but may suffice for the interim until you find a nice high-res version of what you'd like!