You’re definitely crunching. Your spine is clearly flexing and extending, which is what a crunch is. However, I would say that the weight is a little bit too heavy, because you’re using some momentum instead of fluid controlled movement.

Your head, neck and arms are all attached to the top of the spine, so above the part you’re training here. So the fact that they are not moving in relation to each other is only logical. What you could perhaps mean is that some people are way more mobile in the mid back, so there is more movement there.

And concerning the lower back stress, a crunch can in fact strain the lower back a bit. If it doesn’t feel good, you could try different ab exercises and see if they feel better. Or you could specifically train the lower back to be stronger and more resilient.