Make sure you log into your Xbox Live account to see your discount. Offer is valid through 8/31/2015. The offer cannot be transferred to anyone else. Valid for digital purchases only.
A separate Reddit post by DarkRtist says that in a recent chat with Xbox Support they stated,
the developer did not specify that [whether it needed to be purchased physically or digitally] on the price list, normally it should be both, that is why we will be in contact with them about this to verify with them as we on xbox also wanted that the content license is for both for our customers. It will be automatic by the time they will set the license discount for both before the game will be released.
Bethesda and Arkane Studios have not announced a limited timeframe for the definitive edition discount, and it appears this is not occurring for those who previously owned a digital copy of Dishonored for PlayStation 3.