As you already know something about me, I'll skip this part. But I will say that I'm familiar with Godwin's Law.
I think this is a difficult concept to carry off, but think you start off well. It's essentially a slight variation of Godwin's Law (and actually the law doesn't say that a reference to Hitler or the Nazis makes an argument invalid, but that's OK). I have some suggestions below, which of course you're free to not follow.
Prose and Formatting:
I put Humour comments here to avoid repeating myself, but do score them seperately. The parts I found to be the best I would score significantly higher than the score given to this section.
To say this is clearly a takeoff of Godwin's Law would be stating the obvious, so I won't say that. This is an article that likely won't work for those unfamiliar with Godwin's Law, but you probably figured that as well. I don't know that either of those are a problem, though. Is any of this part of the review helpful? Probably not. Let's move on.
How to properly use Godwin’s Law's Law
Bringing Sun Tzu's quote in seems like a good lead in. This part implies that the person using Godwin's Law's Law (GLL) knows what he or she is doing.
On the numbered points, some of these such as 2 and 3 seem to contradict what you've established above. If the idea is that the person is specifically trying to make themselves look bad (i.e. weak by Sun Tzu's definition), then why does 2 say "...is a good way to convince other people of your very valid point of view"? Also 3 says "...therefore make (should be makes) your viewpoints more convincing"? What if the article instead said something like ""...is a good way to convince other people of the vulnerability of your point of view" and "...therefore makes your viewpoints seem more open to attack"?
Potential real life use of Godwin’s Law's Law
"The principle of Godwin's Law's Law can be used even when Godwin's Law is not invoked in the first place...."--this gets me expecting to see an explanation of how this works. I don't see this explanation, and think it would help if you provided it.
"Indeed, invoking Godwin's Law is essentially stating that "Hitler comparisons occur in long online discussions, therefore they are invalid"--this isn't accurate, which of course is fine for a joke article. But I also didn't find it or this section funny. The second paragraph seems to have devolved into standard tongue-in-cheek put downs of illogical politicians and commenters and the like. For example, while I see nothing wrong with "...to protect their sane, reasonable and not at all polarizing viewpoints" in and of itself, it doesn't seem to fit the encyclopedic tone the article established earlier. Also I got somewhat lost in this section. I would like to see this section developed into something that shows another aspect of the use of GLL.
Examples of usage
Here the article uses "Inverted Godwin's Law" as opposed to "Godwin's Law's Law." I think this would work better if it stayed consistent, using GLL or Inverted Godwin's Law throughout (To me, Godwin's Law Law sounds funnier.)
“Hitler supported kitten huffing too! Kitten huffers are like Hitler!”--I think this section would work better if you led up to it; i.e. made some mention before of how Godwin's Law Law could be extended. You could do this in the form of advice or a warning, i.e., "invoking Godwin's Law's Law may have to be extended if your opponent invokes Godwin's Law's Law's Law, which is...." and here's how you do that.
With How to properly use Godwin’s Law's Law (if edited as suggested), I think the article has a very good start to build humour--with the changes I would rate this section highly. Unfortunately, I think it gets rather sidetracked, as described above.
I rather like that Godwin's Hitler mustache doesn't look quite right, but think I might like it equally well if it looked more realistic. I'm torn on that one. I do think the caption could include some mention of Godwin's Law's Law. I like the Obama photo and caption--all it takes is someone making up a rumour to get people to take this stuff seriously. Mind if I say many people are utter fools? Let's move on. I like the Heil Kitty pic and caption.
Average of above
Again, the section 'How to properly use Godwin’s Law's Law really got me thinking, "All right, it should be cool seeing how this gets developed." But I think the rest wasn't as strong. I do believe this is a difficult concept to carry off, but also believe that you can do it. Definitely let me know on my talk page if you edit this.