Are there definitions of the types of NESes according to the four-way theory?
I'm not sure, but I think the upcoming EkoNES will be in a genre of its own, which is interesting. It's a bit of a hybrid I think. Of course, you could claim the genre to be ''FFHNES'' but I don't think that's appropriate considering each of the FFHNESes so far have been very different in terms of game play.
I think that
every NES can be classified according to the four-way theory. Then again, I may be a bit biased on that account.
An Arcader NES lets the players do pretty much anything with their entity, only requiring mod arbitration when players come into conflict. An ideal Boardgamer NES runs like clockwork, only requiring the mod to punch in numbers to the formulas he's already designed. A Simulationist NES has events that follow logically from each other in the context of the game's universe, as the mod sees it. A Storyist NES is a collaborative effort by the players and the moderator to tell stories. These are the furthest extremes of each style, but every NES can be classified on these axes.
Certainly, there are other ways to classify a NES. There are fantasy NESes, Sci-Fi NESes, modern NESes, ancient NESes, character NESes, and as many other types as can be conceived.
The important point here is that none of the four styles are specific to a particular NES theme. Generalizations like "Simulationist NESes are realistic" and "Fresh starts are Arcader-style" are simply untrue. To take the two NESes I'm currently participating in as examples, Pre-ChaNES is Simulationist, but not at all reaslitic. In reality, humanity will not be colonizing the stars by 2100, faster-than-light travel will almost certainly not discovered, and giant humanoid mecha aren't a particularly effective vehicle design. However, in the ChaNES universe, the laws of reality are different than the laws we're familiar with, and events follow logically from them.
On the other hand, from what little we've played through so far, Dr.NES looks to tend more Arcader-Storyist. To answer your question, flyingchicken, I suppose I could be considered a centrist, in the sense that I can (and do) enjoy some types of NES across the board. I don't like most nationbuilding Arcader NESes because interaction between players ends up limited to expansion wars and contests to see who can find the most plausible excuse to have way more Economic Points than they'd ever need. However, I can fully appreciate a setting which is completely illogical while managing to be extremely awesome (case in point:
4 Resident Evil). I even intend to host a light, simple, fast-updating game in the interim between Pre-ChaNES and the main ChaNES whose main constraint is not realism, but coolness. We'll see how that works out.