The native extension you pointed to is not for Push Notifications. Looking at the code for the sample project, the needed steps for Push Notifications are not present. I believe it's for triggering notification behavior on the device from within your app.
A device has to register for notifications from it's parent/native platform's service (GCM/C2DM on Android & ANPs on Apple), then set up methods to handle incoming notifications.
The native extensions you are/were looking for are:
Piotr Walczyszyn's As3C2DM ANE for Android
and
Piotr Koscierzynski's APNs ANE for iThings
The first won't do you any good anymore, because, as you mentioned, you can't register an app to use C2DM anymore.
The haven't tried using the second one because I don't have an Apple license yet, but based on the comments I've read, it seems that he released this ANE as a demo & it's not really made for people to use. He doesn't want to release that version for business reasons or whatever.
While searching, you may find this Adobe Forums post for an APNs ANE, but he won't share the extension anymore. So don't bother asking him.
The last resources I can point you to are:
If you want to use Piotr Koscierzynski's APNs extension,
you may need this help building on a PC.
This is a really nice
suite of extensions for $100 (note that it supports C2DM, not GCM, as of July 4, 2012)
And this is just an APNs extension for $25
So, that's everything that I know / remember that I can share. I'll try to update this if I find any other options worth mentioning. I've already built me app more than 60%, but I basically have to start over now, so ... =/
I'd write them myself, but I don't know Java or Objective-C
=b
Best of luck to everyone who reads this cuz they're in the same boat.
=)
Todd