The linked study demonstrated that injecting amyloid into one part of the mouse brain caused more amyloid to appear in another part. In this sense, the amyloidosis was "transmitted".

The prion-like behavior mentioned is the ability of prions to do something similar. Specifically, a small amount of abnormal prion protein can induce a larger amount to also become abnormal (with respect to it's shape). The process is analogous to crystallization, where small crystal can seed the creation of a larger one.

In the field, the significance of this is that small initial abnormal events can trigger larger ones within the brain, a bit like the famous butterfly analogy in chaos theory.

I believe that Alzheimer's has different clinical presentation than either BSE and CJD, and that the misfolded protein being blamed for Alsheimer's is a different protein than those blamed for the other two diseases.