I have just received my Zenfone 6 today and I can confirm I also have this problem. A loud popping or clicking sound can be heard when I press on the area outlined in OPs photo. I can actually press outside of the area to the right and next to the camera and hear the pop as well.
I did some further testing and I can actually hear a cracking sound when I apply pressure and press down around and directly on the the fingerprint scanner. If I press on the left side it cracks, then pressing on the right side it pops. In fact the whole top 15-20% of the phone is cracking and popping.
It may be a problem related to adhesive because if I swipe my finger back and forth and apply pressure along the area, it actually "sticks" again and the popping goes away temporarily. For around 30 seconds the area feels very solid. The problem is that it pops back out again shortly afterwards.
I was under the impression that the back of the phone is made from glass. Glass doesn't bend and pop like plastic when pressure is applied to it so it does sound like a problem with a layer under the cover.
Also, my phone had the loose wobbly camera issue right out of the box from the first time I picked it up. I did run the calibration tool however it comes loose after some time again. I noticed that after pressing in the area and hearing the loud pop then the camera makes the lose clicking sounds afterwards when the phone is picked up so these two issues seem to be related.
These definitely feel like low build quality and/or manufacturing defect issues to me. I would like to hear from the ASUS support in this thread regarding this issue otherwise I am returning the phone.