The landscape of personality that is mapped in Temperament Theory has a fourth region corresponding to the Idealist temperament, and we would thus expect to find a fourth play style: Diplomatic play. However, currently our research is not sufficiently developed to have any confidence as to what constitutes this play style, and more research is needed. It may be that Diplomatic play can be identified, but that it does not relate well to videogames, or it may be that there is no form of play which relates to the Diplomatic skill set (but this seems highly unlikely).
We can hypothesise as to what Diplomatic play might involve by looking at the skills that have been related to the Idealist temperament. Thus, we expect Diplomatic play to be involved in a process of unifying or harmonising through an abstractive process, and also to be rooted in communication and empathy. This relationship with communication (either the private communication of writing and art, or the public communication that takes place directly between people) suggests that Diplomatic play might be found more easily by examining multiplayer games, but it may also be difficult to separate from Extroverted play.
It is also possible, given the Idealist temperament’s relationship to narrative and metaphor, that certain forms of story play might be opportunities for Diplomatic play to be expressed. But since our current videogames are not especially good at supporting story play, this may be difficult to ascertain. An examination of tabletop role-play might be the best place to search for such a play style. We would expect a player expressing this play style in such a game to be enjoying resolving disputes and conflicts; given the general bias in most tabletop RPG play towards combat, an empirical study should easily show if there was a contrary form of play taking place in such games.