No, you're not
I'm now on my fourth iPhone 6 (dust, dead WiFi, etc), and all four of them have had this exact issue to varying degrees.
Squeezing the display at the edge, over the volume buttons, causes a tiny bit of movement back into the body of the phone. It's hard to see under regular viewing – you kind of need to look down the length of the phone, in bright light, so you can see the barely visible shadow of the screen moving.
And yes, the movement causes a light click. You need to hold it right up to your ear in a silent room to hear it, but it's definitely there.
Just a result of the manufacturing process, I guess, since it's clearly a 'thing' with every iPhone 6, to a greater or lesser extent.
I certainly wouldn't return the phone for it, unless you're prepared to be equally disappointed with the replacement.