I don't really understand how it would reduce processing time, could you elaborate?

The main implications seem to be for neuroscience, as far as I can tell. Backprop is considered biologically implausible because it requires either bidirectional communication over synapses (which doesn't happen) or weight sharing between neurons. But this allows the forward and backward connections to be decoupled (i.e. they are different synapses).

This is really interesting stuff, my first reaction was "why does this even work?" I think I still don't really fully understand what's going on.