【Updated: 】
These are abbreviations connected to course names. You can check them on the driver-selection screen after you've selected a course to race on.
These abbreviations stand for:
SNES: Super Nintendo Entertainment System
N64: Nintendo 64
GCN: Nintendo GameCube
GBA: Game Boy Advance
DS: Nintendo DS
Wii: Wii
3DS: Nintendo 3DS
RMX: Remix