I have been having the same problem, open WD, black screen and then a crash.
I have a fix. From the finder, select Go from the menu bar and select Go To Folder and enter this path: ~/Library/Application Support .
Navigate to the Tell Tale Games folder and delete the Walking Dead folder from within. Now try the game, mine now works.
Don't empty your trash straight away, I don't know where the saved games are stored, if they are stored in this folder at all.