I'm a little unclear on what they mean by exclusive streaming contract. For example on iTunes you can download Disney content and play it locally on your computer or stream what you already purchased from the cloud.
I guess by 2016 Amazon and Hulu are left out in the cold because they don't allow downloading of videos just streaming of content.
I think if it's a separately paid rental or purchase, you'd be able to stream it from that service. What this is for, is for subscription streaming exclusivity (which means Disney would not stream on Amazon Prime's subscription service, Hulu Plus, etc)