So what did the drogue chute "grab on to" then?
Don't know if you were being sarcastic or not, but here goes. At that height there is of course a residual atmosphere, the drag chute created enough drag (nomen omen) to stabilize Kittinger because:
- it had a much larger area than its cargo and a regular shape (conical), making it inherently stable
- because of the geometry of the whole thing, with Kittinger "hanging" from the chute creating even more stability, much like a ship with its ballast at the bottom of the hull
Add to that the fact that the full pressure suit that was in use at the time was as stiff as a board, making it impossible for Kittinger to move his arms and legs in order to stop any incipient spin, like a normal skydiver has to do all the time or he will start spinning soon enough.
Baumgartner's suit doesn't look like a full pressure setup to me, maybe he has enough mobility to control his attitude. The video material currently being released only shows him stepping out of the capsule, we don't know what the first few seconds of freefall look like.
Ciao,
Dg800