That's interesting. As far as I can see they're not linking it to inactivity but specifically to that posture.
It's interesting to me from the perspective of having done Alexander Technique where there is an emphasis on re-educating people on how to get in and out of chairs and how to sit in them. This simply because few people do it really well -- chairs seem to encourage unnatural postural habits.
I suspect people who sat cross-legged or in lotus, etc. (or who squatted -- sat on their hams) might not have similar increased risk of mortality. I think this will be not sitting simpliciter but sitting in chairs.
There's a lady who's both a Professor of Architecture (at Berkeley) and an Alexander Technique teacher who has a book on the chair that I keep meaning to get around to reading:
Amazon.com: The Chair: Rethinking Culture, Body, and Design (9780393319552): Galen Cranz: Books
One of the things people often do in chairs is slump against the back-rest with their shoulders and upper back but with the bottom forward -- often sitting on the coccyx instead of the ischial tuberosities (sitting bones). The back-rest of a chair unfortunately provides a stimulus to do just that.
Among other things, this compresses the abdominal area. That's going to squash up the internal organs, and how is that likely to be good for you? It will also interfere with respiration: if the diaphragm can't move freely, you can't breathe as deeply as you would.