To install the files associated with Myst III your computer should have an OS 9.1 partition. The Myst III files for OS X require your Myst III version to be v1.22 and your OS to be 10.1. After updating your OS with Apple's OS X update to 10.1, you will need to install Myst III: Exile and the v1.22 upgrade. Though you may be in OS X, the upgrade will install a new shortcut to Myst III on the desktop of your OS 9.1 partition. This can be copied over to your OS X desktop.
Lastly, there are two files you will need to add to the Myst III folder to run the OS X version. Extract the Myst 3 OS X and Bink Carbon Library files from the M3OSX1.sit file. Then place them in the Myst 3 folder. You can delete the original Myst 3 Exile (US) and the Bink Shared Library, as they are no longer needed to run in OS X.
* Mac OS 10.1, OS 9.1 partition
* Myst III v1.22 English
At long last, Myst III comes to OS X. The updater has a bug - it only searches your startup disk, at least when run in OS X. I had to copy my Myst installation there. It doesn't seem as sharp as in OS 9, but I haven't played in a while so maybe not.
Anyway, it works - woohoo!