I think the magic ARS "Abstraction, Realism, Symbolism" Triangle works with an indicator for the used resolution as best thing to exactly point out where styles are.
Helm's description in the ramblethread with the triangle explains things much better than some of your crude "words" which selection is rather questionable.
IMO:
I don't really think your style overview is accurate. On the one hand you'd call "professional" a own style. Usual professional artists are just artists who are making a living with their art. Their style can differ vastly, as long as they sell their stuff they are professionals.
I also won't count "popular computer games" as an own style, because they were made as computer games and because of various reasons they got popular, which doesn't mean that all of them share the same graphical style - after all it's art made for games.
Animation is an art itself, it has it's own rules and it's own impression. All animated pixels will have motion. All animations will have their own distinctive style. Animation has it's own subcategories and pixel animations are one of these with own subcategories too (as ErekT said). It's pixel art, but mainly it's an animation.
Isometric is rather a perspective than a style. Just because it's an perspective it doesn't mean that it couldn't appear in any style. There are lots of flat shaded more graphical isometric pieces and some more realistic shaded ones.
As you see there are already lots of term which are suspending or overlapping themselves partially. Some of them explain rather techniques than styles.
Of course different artists use different techniques to achieve different effects. Techniques like AA, dither, cluster-control, clean lines etc. are just related to the pixel tech.
Techniques like perspective, shading, color theory, composition, anatomy and a lot more are related to drawing tech.
For pixel art you need to master all of them, how you balance them is every artist's own decision.
I think that the key for how we can apply these techniques is resolution. If the resolution is too small and there is no place you are restricted which causes a distinctive style. 8x8 sprites don't use excessive dither or AA because there is no space for it. Even if a great artist with a well-defined style would work on a resolution like that he'd have to heavily adjust his techniques to the resolution restrictions.
If the resolution gets really big and you use a lot of colors you usually can get a much more realistical rendering than on a smaller resolution with less colors, that at least should be common sense.
The resolution however don't affects the idea, it's more that the idea affects the resolution. If someone works on a bigger resolution and don't wants to render realistically and uses the more graphical approach it's usually because he wants to have "that" distinctive look. So the "Bubblegum" as you call it is just higher resolution with more abstraction than realism.
A good example for this would be Pistachio's werewolf edit and delicious' final werewolf.
As you can see Pistachio tried to apply a lot more painting technique with interesting structure, realistic shading and clusters which look more like concept art. The edit isn't polished, but it's much more realistic than Delicious final rendered "Bubblegum" end result which throws most of the advanced painting knowledge Pistachio applied over board and concentrates much more on beautiful clusters (the subject and the proportions are exactly the same, the rendering is by far different).
I'd say that delicious'- wolf has a more "graphical" approach while Pistachio's wolf has a more "realistic approach" (which tries more to look like a traditional painting or photograph instead of a vector).

I think that delicious' wolf would also work good with the half resolution (if there would have been a restriction in terms of resolution) while pistachio's final rendered wolf would most probably need the size to apply all the details needed to achieve the realistic feeling he sketched out.
If you'd resize both of them delicious wolf won't loose a lot of detail while Pistachio's wolf definitely would.
Delicious wolf although would also work really good with vectors (and would most probably look much smoother)
The more pixels you have to illustrate something the smaller the need of simplification is. Simplifying things to optimize your workflow or getting a more unique rendering is just a matter of the idea or the need of the graphic.
I think the magic ARS "Abstraction, Realism, Symbolism" Triangle works with an indicator for the used resolution as best thing to exactly point out where styles are. It's possible to clearly put in every artists pixel work.
It's basically the same as if you'd pick colors.
If there is no indication for the resolution it's hard to say if the look was caused by restrictions or if it was intented by the artist.
Like the werewolf example which is pretty much a high resolution strong abstracted piece of art there are pixels which are low resolution but try to use as less abstraction as the resolution restriction allows.
Helms initial post I built on:
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As mentioned before, the goal of the pixel craftsman is twofold. On one hand he tries to make the apparent resolution finer. On the other he struggles to represent what it is he's drawing. The two goals are always in friction. Let's look at these two pieces of high art I just devised:

And this:

I posit that both images represent the same idea. A man shitting in a sine arch.
The first image has a high apparent resolution because the lines are perfect and also - more importantly - because as the viewer looks at this they cannot discern a pixel grid, they cannot see the single pixel almost at all.
In the second image the single pixel is very apparent. If we zoom in a bit more in fact,

That there is a very confined space in which to represent the human figure in its volumes and shapes means that the more colors and clusters we employ, the more the underlying grid of the image has to show.
The particular ambitions of the pixel artist, at this level, are paramount. If one wishes to convey a fully rendered object as realistically as possible, it cannot be helped that the apparent resolution will be lowered. As clusters of pixels come to interact, places where the pixels 'line up' and betray their resolution are inevitable. The trade-off is that the rendered object appears more realistic, with whatever benefits the artist might assign to that. Let's look at a schema:

Here we have a simplified model of aesthetic motivation for the pixel artist. It isn't very different from the motivations of artists in other fields, but there are some additional considerations to inspect that are very pixel-art relevant. On this point I'd like to say that I am not using the above terms as they're usually meant in the history of art. I am appropriating the terms slightly so the layman can follow along.
With abstraction I mean that the realized object of the piece of art does not clearly refer to something in the natural world.
With realism I mean that the artist is attempting to render his object lushly enough that the viewer will interpret it relatively literally.
With symbolism I mean that the artist is attempting to convey objects with clear higher functions without allowing for literal interpretations.
Try to think of your favourite pixel artists, and place them in a space within the triangle. Try to assign specific works by them in the triangle and then make specific observations about how each artist is prioritizing their two goals: hiding the grid/increasing apparent resolution and conveying the volume, light and surface of their intended object literally. You will find that artists near the top of the triangle will have very high resolutions and very simple/naive objects, whereas artists near the left end of the triangle will have resolutions of moderate fineness while their objects will be meticulously shaded. Art towards the right edge of the triangle will both have very low resolutions and very simple shapes!
The realist pixel artist will often make large areas where the resolution is practically infinite (like the shoulder of the girl in the above Lazur bit) and then place single-pixel, low-resolution level detail on various specific pieces to rejoice in the pixel-ness of his work just a little (the highlights on the hair here for example). The ambition of the artist leans heavily towards removing the grid, but doesn't frown away from going 'hey, here's my pixel, do you love it? I love it!' once in a while.
The complete abstractionist has effectively destroyed the pixel in his work, it is in the place of Ideal Space. It could be vector art or anything else that isn't shackled to the limitations of a monitor really. We do not have examples of such pixel artists really because as you might imagine, that goal would be very self-defeating. However there are a few artists whose work is very very close to vector smooth, like Panda or Ilkke sometimes, but you can tell they're pixel artists at heart because they can't contain themselves from putting in pixel-level details in a few places after all.
The symbolist pixel artist creates art that is very informed about its being made of pixels and wants the viewer to know it also. All of the modern 'retro art' fits in that edge of the triangle for me, with the artificially low resolutions and the flat and fat pixel character designs. These retro artists are not interested in pixel art technique to make the resolution higher, they are interested in invoking nostalgia on the older viewer or to inform the younger viewer of the semiotic particulars of older video game art.
I do not judge any of these motivations. It is however my belief that regardless of which way the artist might feel drawn towards, for their art to maximize its capacity as pixel art, they should reconcile their different aspirations so as to retain a place within the relative center of the triangle (the grey circle area). The realist artist should not attempt to completely abolish the pixel-level detail and end up with a blurry mess of a piece with 250 colors in it. The symbolist artist should not completely forego the attempt to make their pixel clusters achieve their ideal state. The abstractionist should not make their resolution that fine so that in the single pixel no longer feels like it belongs.