It does, actually, but in a way it also doesn't. I could go into roleplay theory for hours; I've spent ample time studying papers published by the Meilahti and Turku schools as well as became well-versed with GNS theory as well as basically all theories derived from the threefold model. I followed Ron Edwards for a long time after I immersed myself in tabletop-style roleplay, as well as simulations thereof (such as Baldur's Gate, Vampires: The Masquerade, etc.).
I would boldly say immediately that because this is purely text-based roleplay, it must be addressed with such an outlook. GNS theory would logically say that pure-text based gameplay focuses on the narrative, but the facts are there are still gamist and simulationist aspects, as well as several other factors. In short, when applying any of those theories, it must be done intelligently and with careful, careful forethought.
This is just the way I think. I use pre-existing structure and guidelines to understand things, including stories, books and literary technique. I believe at one time I even questioned debate technique. It's because there is, in fact, a formal way these things are done and observed for the sake of maximum effectiveness and understanding in an objective view.
Roleplay, whether it is an art or not, is no different. In any art class, you learn that there is a different between looking at art and seeing it. You can look at anything; you can even look at things subconsciously. But, seeing something involves the applications of memories, feelings and logic as you perceive it and that is the definite difference here. In this situation, I look at these aspects and these interactions using my memories (what I've learned through study) and logic to understand better what is happening, although I must admit as anyone should that I do have personal feelings and biases to some things. Just a fact.
When looking at 1x1's, I stop labeling them. It's important to understand what makes a 1x1 different, what the category is, instead of just titling it and moving on. A 1x1 is, most commonly, a roleplay without a formal moderator and with only two roleplayers. This is important because, as you just showed, you only looked at the number of people in it, not their relationship to the roleplay. It's true that I did the same, but that was because I was addressing the point of why I believe 1x1's get stale.
If you add a third person, you add in a whole new element. Once there are three, what if one person would prefer making plots, NPC's, etc. instead of a single PC? Does each person need to focus on a single PC? I've seen 1x1's, as I've just described them, that have the roleplayers against each other as often as they team up. What if it becomes 2v1 in IC, is it 2v1 OOC? If not, how are situations determined? If one person creates the main conflict, are they not an informal moderator in the sense they're mostly influencing the plot and setting?
In short, a 1x1 exists as it is because it is incredibly simple to create a roleplay, setting and plot that in general focus on two characters. The addition of a third changes the dynamic in the sense that it limits a few possibilities due to the complexity of their nature. I said before that a 1x1 limits interaction, and this is essentially what I mean. With the elimination of a large chunk of interaction and plot dynamics, you simplify an incredible amount of the roleplay and eliminate many of the leading needs for Moderation.
But, let's go back to why you are in fact on track in my opinion. With three roleplayers, you increase interaction, but you also create the need for more structure. All you have to do is create that structure and answer the questions that arise. If done cooperatively, you eliminate the need for further moderation and you can address the plot, setting and roleplay itself as it matures, and even reassess how things need to be ran or how the structure should be. Now, what did we add here? Was it just another player? No.
We added structure. We created something like an access point to a roleplay where a third person can come in and be part of it, and that's a huge task as well as a huge observation to take note of. It is neither an easy task or a common one, but it is possible and as a matter of fact it's the reason that most of the time roleplayers seek out the structure from the very beginning. A 1x1 rarely becomes a 1x1x1, yet a large roleplay can be dissolved easily into 1x1's and often times you could have multiple 1x1's existing within the same plot and setting but never actually interacting on an personal level - that's a hugely advanced roleplay concept most often called non-linear networking.
But I do digress and pose the interesting query: if you added a bit of structure to add a third person, what do you do for a fourth? Logically, you do the same. At what point does the structure become too complex, time-consuming or just--plain tedious for the group to do? At what point is there a need for an actual Moderator? A GM? That is a personal question related to personal preference; something I talk about a lot. If you stop looking at 1x1's as a different genre, it's a lot easier to see a relationship like this. Overall, compatibility, patience, attitude, creative outlets and personal preference all play huge roles in this. I know plenty of people in 1x1's that don't like the idea of only roleplaynig with one person as much as they just dislike the idea of a Moderation, whether they're polite or overbearing.
A whole different topic is one called a "Shared World", which is an incredible tool and roleplaynig concept, but it is rarely effective. If used, it has the potential to create large, interesting roleplaying scenarios, all bound together with a single context. A prime example would be Mizahar or any Final Fantasy and/or Naruto themed roleplay forum. They're a-dime-a-dozen, but they all have these immense amounts of characters and plot sharing the same setting. A 1x1 scenario here on RPGuild has nothing in comparison to the immensity, and that is because social engineering here is definitely meant for the small scale. I pose the thought that the social status here doesn't at all mean it is the best or most effective, merely serves a purpose. Some of the points I made here should easily highlight that.