Matt Graham of Graham Combat covered the topic of "shooting while moving".
I like his no nonsense approach to the subject. There isn't any secret ninja or Apache style of
walking to do, just walk normal.
However, with a handgun in hand while shooting, you obviously want to minimize the front sight
bounce. This is the method that Matt instructs, be conscious of the muzzle bounce and walk normal.
This concept was also demonstrated with the AR as well.
Here's a brief video of Matt teaching Shooting on the Move.

http://westernshootingjournal.com/tactics-tips/shooting-move/

Do you work for Western Shooting Journal or something?

I've seen better results, for me and students, when doing the things he says don't do.  Different strokes and all that

Before watching the video, lets Google the guy up and look at his bio....





"serves as a civilian defense contractor functioning as a full-time
firearms and tactics instructor of protective and low profile
operations. As a former federal air marshal, Matt operated covertly
throughout the world, running low profile counter-terrorism missions.
Post 9/11 Matt served as a Department of Defense security contractor.
Prior to 9/11 Matt worked patrol as a police officer, both municipally
and as a county deputy, and is a recipient of the Life Saving Medal, the
Medal of Valor, and the Law Enforcement Medal of Honor. Graham Combat
training courses, all created from Matt’s experiences and taught from a
concealed carry profile, are a blend of these operational backgrounds.
Matt has designed core curriculum for defensive shooter’s focusing on
fighting with what you carry, shooting fast, and hitting first."
O.....K.....  





Watched video...
meh.  Sounds like another guy doing things "different" just to be different.  
Here's how I do it...   Second video's show how pro's do it...  Second video notice no one "just walks"...












 

Yeah, that advice has its issues and merits. If you're just going to take some guys and want to get them on paper without having to worry about basic fundamentals- then sure, just walk towards the target.

Now, just like any other techniques in shooting, there are basic fundamentals. Remember the 2 firing tasks. 1- Properly point the weapon at the target. 2- Fire the weapon without moving it. Anytime you walk normally, you are transferring weight and shock loading a foot. This causes issues with Task #2. You have to have smooth weight transfer. You need to roll from heel to toe on your outstep. It isn't Ninja magic- it is basic fundamentals. And that is exactly as it is taught to prospective Tier 1 Operators. Because it works. Failing to do this will induce movement which will clearly be visible in the the sight. You will also see shots dropped to the 6 o'clock because of shots breaking when the heel comes in contact with the ground.

"Simple" techniques like the OP mentioned are popular in the industry because it represents an "easy" button to shooting like an Operator.

The "simple" truth is there is no easy button. It is all fundamentals, and you have to invest painful amounts of time into the minute details of every aspect to establish a solid platform of skills to fall back on when you aren't performing the tasks on a clean flat range at 15yds with the lights on and nobody shooting back at you.

I've taken 3 pistol classes with big trainers (big names) and 2 pistol/carbine classes.
None have done any shooting on the move.
I'm REALLY hoping the 2-day Mike Pannone class does some, since I can never do it on a gunrange nearby.

Sorry slow deliberate steps directly at a threat is a good way to get yourself lit up. Total opposite of what I have been trained and common sense. You should try to engage with fire & as quickly  as possible move   to cover.