My guess is they're using the applet to run the P2P program and the Flash client to connect to various P2P "servers" over HTTP (or possibly) RTMP for streaming.

I don't think you can bind to local ports and run servers inside AIR or Silverlight, but you can in Java applets.

They could theoretically have 100k P2P Java applets running on "super node" (high bandwidth) machines serving an audience of millions of leeching peers. Hopefully they've realized this. It's probably the best way to mitigate the applet problem: only require 10% of people to have it.