I suppose what he is saying is that the crystal creates an electric current in some conductor. That conductor then has an electric field around it. If you had some charged particle nearby there could be a force exerted on it. That author then says "charges accelerate and collide with air molecules". Strictly speaking this is true.

But this description sounds more like a particle accelerator and less like anything to do with radio waves. All of this stuff is irrelevant. As you've pointed out, you could just as easily put the crystal in a vacuum and get RF emissions from it.