Why G Does Not Light Up In Network Cable Tester?

There is nothing wrong with your tester.
There are 8 strands in an unshielded network cable which is what you tested in your video.
A shielded cable also has a grounded metal sheath surrounding the 8 strands. The G on your tester refers to this.
I have a similar tester but in mine the shield is referred to as "Shield".