Actually in recent months I heard a different theory. According to that link you posted, a Type 4 is just the top level achieved routinely in science fiction, frequently by humanity - ie free and easy domination of the Universe. By that definition the Federation of Star Trek are Type 4.
In Isaac Asimov's Extraterrestrial Civilizations (Crown, 1980) he discusses a classification of possible alien species which went as high as "Type III", where "Type II" would have the power to dim their own sun, and "Type III" would have the power to do that to a whole cluster of suns (thus sending us a signal we could see and recognise as intelligent).
However, the theory I heard recently basically took as its basis a concept from The Matrix, that eventually civilization would evolve to the point that people could live whatever simulated life they chose. The theory then further went on that, what with the age of the Universe, the infinitude of stars or whatever, they had calculated that the odds were very high that not only had a civilization done this, they had furthermore gone on to simulate entire Universes - and that we ourselves exist in one of these simulacra. If the definition of Type 4 is simply the ability to control large portions of our Universe, then surely the creators of technology-based perfect simulacra Universes would be Type 5.
I'm also surprised at Brutus1964 bringing this up. To answer his basic question as regards myself, however, I would rather not believe in such God-beings and believe that everything in the Universe I see is naturally occurring, than have to accept that our Universe is a created simulation and that it is the creators of that who evolved totally naturally.
Belief in God began because of the natural inclination to see the world as something created. As we explored and examined, we found less and less evidence for supernatural creation, but simply the result of immutable, natural laws. Once you have that paradigm and realise that everything (life, galaxies and stars, the entire Universe) occurs just because of physics, you are left with less for God to do until He just creates the Universe at the Big Bang - but furthermore you are left with the conundrum that since you have scientifically explained nearly everything, you have the question, "If God created the Universe, who created God?" If everything is explicable through natural laws, how can you use non-natural means to make the final step of Creation itself?
And this is why I'm not inclined to accept God-Being theories, since it just defers the point of origin, and you might as well face the ultimate God question straight away.