Ok, I only skimmed the paper but it seems like all of the "non-local phenomena" in support of their theory are basically psychic powers. Not exactly strong evidence.

You're free to stop there. We can also turn it around, and I can ask you for any paper that details the theory of why the brain should be the location of consciousness.

I only gave one example and Wikipedia to start with. There's a lot of material out there if you're (rightfully) skeptical of that one paper. I don't even know what you're refering to as "their theory", as the way I read it, they're basically documenting various co-existing theories, and the authors don't disclose which one they find the most likely. I also don't see it as necessary for science to pick one; it's all about theories. I prefer documentation of all possible theories, and see no reason to dismiss one over the other unless they're disproven. I pointed to that paper, because any paper that talks about alternative theories shows the point I was making: We don't know yet. The point was not to claim that they've managed to put together good or bad arguments.