To install illumineX software for Mac OS X, simply download the disk image (.dmg file) using the download links on various pages, like this one for ecto.
When the image is downloaded to your hard disk (probably on your desktop) you can double-click the file and it will get added to your desktop as a software "disk" with the name of the game. Open the "disk" and you will see the application icon. Drag this icon to somewhere on your hard drive (we suggest the /Applications folder).
When it is done copying, eject the software "disk" and then drag the dmg file to the trash.
In addition, after installing a game, you can choose "Check for Updates..." from the game's application menu to check for and download updates to the current game.