Possible fix

Well they didnt post my bad review so I hope they post this one. This is what I received from telltale.
First, please fully close the game app and all other apps running in the background of your device by double tapping the home button and swiping up on the apps. Shut off your device for 10 minutes to allow it to cache. While it is off, please reset your modem and router to refresh your WiFi connection.

Turn your device back on, then go into Settings and turn the WiFi Off, then back On again. Log into your Apple account, launch the game, and see if you are able to continue to the main menu as intended. Please note that a black screen may persist while the game is installing updates. If you still receive a black screen when the game is checking for DLC, please allow it to remain on this screen so that these updates do not get interrupted.

This worked for me. I was stuck on episode 2. No problems thus far and I am on episode 5 now. Be patient with black screen. It doesnt go away right away but it will play.

Hope this helps!

Nce101 about Game of Thrones - A Telltale Games Series, v1.6