On Mac or Linux, first connect with Bluetooth by holding down the Sync button inside the battery cover.
The fact that I had been able to play a GameCube game on the Wii was a signal that the two were very similar, hardware-wise. WJoy: Nintendo Wiimote driver for Mac OS X. It took a few hours of experimentation but I finally figured out how to play Wii games on my Mac. After a bit of research I've found that Dolphin, the emulator I found to play Gamecube games, can also emulate Wii games.