Netflix and Amazon know the days of physical discs are numbered. I don't think Amazon needs to acquire a business to dominate a dying vertical. They already have digital distribution and a huge brand, just bank on that.
I agree DRM is shitty for purchased movies, but this is basically a pay-per-view service. For most movies that's all people want. Why wait for the mail man or go to a store/kiosk when you can watch instantly from your couch?
Also, Redbox is booming - and they have 10,000 "physical distribution centers" and don't even carry Blu-ray.