Is the Force Touch Trackpad on MacBook Pro supposed to be 'nudged' with a mechanical clicking sound?
The video quality is such that the nudge is not really visible. But yes, the intention is that the trackpad should not physically move in normal circumstances.

The clicking sound on the video however sounds pretty much like it should. The sound is generated by the computer - it is not mechanical.

You could consider taking the computer to a store and comparing the sound with another MacBook Pro.