If you wanted to get Titanfall Xbox 360 via Games on Demand, that won’t be possible as the game is a retail only release.
EA has confirmed that the following concerning a digital release for Titanfall Xbox 360:
After extensive testing, we felt that it simply did not represent the true Titanfall experience and it was decided not to release a Games on Demand version.
As we never officially announced that Titanfall would be available via Games on Demand and the option to purchase it that way should have never been offered. We hope players understand this decision was all about quality and making sure you get the best Titanfall experience.
This is an odd decision since the Xbox One and PC versions are freely available to purchase via digital download.