but also with the deck pogoing up and down like a Clash fan in 198
Size matters, size matters.
I suggest the author of the article takes the Stena Superferry between the hook of Holland and Harwich. I have done the crossing in a level 6 storm and you could not feel a thing. If the landing barge is big enough it should indeed be OK for a reasonable storm (I would not try to land on it in a tropical hurricane). It also depends where you land. The beauty of sea launch and recovery is that you can do it anywhere. While the Indian and Pacific oceans always have a sizeable wave, the Atlantic puddle quite often calms down to a nearly-lake state (especially in the tropics).
As far as wings... these are not wings, these are aerodynamic control paddles same as on the ESA reusable "spaceplane" project. Nice design - should allow the rocket to use less fuel during the return phase.