It connects via the high speed parallel port at the bottom of the GameCube and requires use of a boot disc to access the hardware.
A special Game Boy Player for the Panasonic Q (SH-GB10-H) was released because the Q's legs are oriented differently from the original GameCube's.
The Wii has a substantially different footprint, making direct compatibility too complicated to be included.
This allows a sort of co-op mode for games that do not normally have it (this was most likely not intended by Nintendo).
Before System Menu 3.0, the Wii allowed unofficial GameCube software, such as this and Action Replay.
As the dongle plugs into the Memory Card Slot, it was fully compatible with the Wii.
[3] System Menu 3.0 prevented unofficial GameCube software from running, rendering this unusable.