Are prophecies magic in origin?
Probably not, though the method used in recognizing or predicting the events prophesied would be. Certainly the power that transforms a vampire into a normal human would involve some supernatural force. As has been pointed out, magic has been restored, but it isn't the same magic as before (maybe the equivalent of Coke vs Pepsi) so what was supposed to cause the Shanshu would be at different, if not eliminated altogether.
For example (though I'm not suggesting any of these alternatives specifically:
1) Angel would become human, but retain all of his vampiric powers.
2) He may become human by being literally reborn or reincarnated, thus having the opportunity to "start all over again," and live an entirely new life from infancy to old age with or without any knowledge of what his prior life and unlife had been.
3) It may be something like what the Powers did in previously, but instead of making a single day rerun, it could take him back to the moment just before he met Darla, and change everything from that point forward, making him Liam once more.
4) Or, my personal favorite, he wouldn't be a vampire anymore, he would become an immortal 4 armed monkey and be assigned to guard the Watchers' Library during Fray's time as Slayer.
(Just kidding on that last one, Bangels, put away the tar and feathers)
Point being, the Shanshu was supposed to be that a vampire would be of such a great service in an apocalypse that he would have his humanity restored, but that was under the old magical system. It might not exist at all under the new system, or might be significantly altered.