It's definitely different from 3D illusions, yeah.
The depth is extreme. The yellow is at what should be the 'right' depth, but the blue is way further back and varies based on its shade. And... no, there's no lack of parallax... it feels totally natural.
It depends on the picture... sometimes I can't see it 3D at all, sometimes I can if I 'try' (I don't really know what 'try' means though... it's not at all like 3D illusions) and sometimes it's so overt and strong that I can't even perceive it as 2D (like the Swedish flag picture).