Your use of TM was good, but the point I was trying to make is that when you restore an application, you are restoring it in the /Application folder.
A lot of applications create a separate folder in the users home folder to store user related items like preferences, game results, etc. Restoring an application would not restore items related to the application in your home folder.
I'm guessing there is a file in your /User/Library/~ path that contains information for your game, including your "career mode" data. That is the file you need to restore.
Edit:
For example, if the name of your game is "StarWars", search your /User folder for a folder called "StarWars". If you find one, that is what you should restore.