That's the challenge on these message boards. For every 50 posts full of crap you'll only find one good one - and that's on a good day. If you look at the diameter of the pipe that is currently spewing oil, and then look at the diameter of the top of the dome, as well as the slot in the one wall of the dome, you have a larger cross-sectional area to relieve pressure. Thus, oil will escape out of the dome until they put negative pressure on it, at which point the oil will tend to float upward and will travel up the pipe. But as they noted (and I'm assuming you understand standard temperature and pressure theory) the cold water coupled with the high pressure could result in icing in the pipe - that's why they have the warming collar on the outside of the pipe.
I think they have some kinks to work out but I do think they have a legitimate shot of making this work.