So it looks like Island Rum has successfully downloaded the game, etc but something is going wrong when it tries to launch City of Heroes
Go to Finder, in the menu choose Go -> Go To Folder and paste "~/Library/Logs/Powermad Software/Island Rum/" in the box that pops up, in there you should see a file called "Player.log", open it in a text editor and have a look at what it says, especially towards the end.
If that does not help you, reply with the contents of the log file (in spoiler tags please)