First off that guide is taken from XDA, the go to site I use for all of my Android devices, and it;s the one I recommend all the time to anybody looking to root, flash ROMs, and other things with mobile devices.
So yes, that guide will work for you.
Rooting is basically allowing you root access to the device. Allowing you to change pretty much anything on the device. Whether it's good or bad, the choice is yours.
"With great power, comes great responsibility."
With rooting your device you are trusting that the developers that make apps that ask for root access know what they are doing. With root access they have access to all kinds of things they normally would not.
As far as bricking your device is concerned, it's hard now a days to "hard brick" your device, but it is possible. The more common "soft brick" is easy to recover from. Often times a simple flash of a stock image will undo everything you did. IT is available from Nvidia, and can be found here.
Would the method shown above definitely work with my device?
Could this method brick my tablet?
Technically yes, but the chances are slim. Faulty cables, power outages, and others could cause the process to fail.
Is bricking predictable - does it happen due to something done wrong or can it happen randomly by chance or depending on different things?
What can cause the device to brick?
Bricking is caused basically when you mess up the ability of the phone to boot into the boot-loader or accept commands from a computer. Many other things will prevent the phone from working, but other stuff is usually easily fixed. The big problems are caused by something going wrong while the boot-loader is being altered. If you kill the boot-loader, there is no boot-loader to get to where you can fix things. This post explains it pretty well.
Is it very likely that my device will be bricked?
Once again, slim but anything is possible.
What do I do if the device becomes bricked?
If you can still get to the boot-loader, start the process over again, flash the stock factory image from Nvidia. As long as you can get to the boot-loader, the device can be fixed. 9 times out of 10.
What precautions should I take and things should I do before, during and after rooting my device?
Use the cable that came with the device. Make sure the device has at least 70% battery life before starting the process.
How can I stay safe while the device is rooted?
Only install and allow root access from apps that people have posted about working as intended.
Would rooting mean I lose functionality to some stuff on normal Android i.e. Google Play and Internet?
Rooting could cause some functionality lost on certain devices. But I have the WiFi only version of the Nvidia Shield Tablet and I haven't lost any functionality at all.
How could I unroot my device?
Most of the superuser apps(controls what gets root access and what doesn't) offer unrooting options in their settings. I know the app SuperSu does.
After this how would I re-root it again?
Just repeat the process again from the guide.
Feel free to ask any other questions you might have.