So, apparently there was an update to the Launcher. Except, instead of replacing the binary, it created a copy in a different location.

If you had the launcher in your Dock and try to launch the "old" version, you're greeted with this message:

And, as you can see, the new one launches as a separate icon (with the previous version's icon still in the Dock):

Is this because I clicked "Quit" instead of "Relaunch" when it updated, or is there just some noob working on the team? Blizzard has been making Mac OS X launchers for how many years now? They should know how this is supposed to work by now =P