Found below are the myriad of races found in the Shining world. Some might be less recognisable and/or conventional, but any may be used as wanted.
Human
Beastman
Birdfolk
Catfolk
Centaur
Dragon
Dragonfolk
Dwarf
Elf
Fairy
Foxling
Half Giant
Halfling
Kyantol
Magic
Creature
Ratfolk
Robot
Wolfman
And by no means do you have to restrict yourselves to the selection here. For example, Shining Force: Ancient Pathways makes use of an avariel character (a winged elf).