The eye is simply one of many strange physical distinctions badguys in Bond movies (and books) have. They physical difformity is an illustration of their moral depravity. Like many of Fleming's characters, Le Chiffre in the novel was very fat, ugly and redhead (a sign of malevoleance in folklore). Instead of being a complete monster, they simplified it by having Mikkelsen's Chiffre stuck with a bleeding eye.
How did he get it, by the way? Any idea?