How it worked for me:
1. Start Saints Row: The Third.
2. Select Downloads from the main menu.
3. Select Season Pass downloads (Something like this, I'm doing this from memory).
4. This brings up the Xbox Guide interface from where you download Genkibowl.
5. Wait for the download to complete. Don't do anything else.
6. Select Continue from the main menu.
7. You should get a notice that Genkibowl content is unlocked as soon as your game loads.
8. Select the first mission from your phone to start playing it.