The ROOTING process for the Z1 Compact has been completed.
It did not work with the method of the video in the previous post because that method is not meant for Z1 Compact. I tried to used a method of a similar phone but it did not work. It caused the O/S to stop working completely.
I learned that Sony has provided official tools on their support websites that can unlock most if not all the Sony Xperia phones bootloader. They also provide tools that work on Flashmode which is used to restore any corrupted O/S but it only works if the bootloader is unlocked. I tested these methods on both of my Sony Xperia phones and it worked well.
The method that did work but also needed to find some of the requirements separately is in the below video.
Unlocking the bootloader did cause all the settings to reset.