Looks like a single pivot. Progressive suspension is designed to have less resistance in the beginning stroke to soak up bumps and get progressively harder to compress so the shock doesn't bottom out harshly. If in fact your seat stays are flexing so visibly as you state, one reason could be inferior layup of the carbon fiber. Designers that understand the properties of the material can fine tune strength-to-weight ratios which allow the designer to ensure extra strength is applied where need and weight is reduced where appropriate.
To answer your questions: No, the amount of distortion you mention is not normal, it is not a "design element". Yes, this frame may very well fail if you are accurately describing the amount of flex you are observing.
I would find out what the torque recommendations are for this frame, get my torque wrench, and double check all connections, as well as rear wheel to frame. If your shock is not properly installed, your rear end will flex.
Another possible and very probable explanation is misalignment of the frame.
Lastly, your shock may be faulty, resulting in your rear frame getting jacked up as it attempts to cycle through its travel but meeting resistance. But I don't believe the rear triangle should distort like you describe.
Take your bike to a trusted bike mechanic, have him or her check the alignment of your frame. I'm guessing this is an alignment issue. Be safe.