There are a couple things I looked at with some concern. First and foremost, the winds, while they were moderately high, they did not seem to produce wave heights that would have been threatening for a boat of that size. Therefore, the waves passed harmlessly beneath the stern without coming over the stern and entering the cockpit. Had the winds been, say, 45 to 50 knots, I suspect deploying the drogue could have caused sufficient slowing of the boat to send waves into the cockpit.
Additionally, they seemed to be sailing in the same direction as the storm front, and it appeared as if they were making a fair amount of speed with just a storm jib. While I have, admittedly, absolutely NO bluewater sailing experience, I have researched the subject extensively over the past three years. From nearly everything I've read it is foolish to run with a storm, or to attempt to outrun a storm. If you're running with the storm you are essentially extending the time you will be exposed to those conditions by a significant margin. Trying to outrun the storm is nearly impossible, and pretty much accomplishes the same as running with the storm--you'll just get the hell beat out of you and your crew.
Now, I wonder how that same boat would fare if the drogue were deployed from the bow with a harness while hove to? From what I've read I would tend to believe that this would be a far safer option in storm conditions. Under those circumstances you could spend the night comfortably, but very slowly drifting, thereby allowing the storm to pass over you and when conditions improve, sail on to your destination.
Just a though,