This definition goes back to the French anthropologist philosopher René Girard and might answer the question why theatre (still) exists.
Somehow the notion of "rivaling dynamics of mimetic desire" makes me think immediately of how marketing strategies work. They are not only a tool to stimulate all kinds of endless new desires but also to control its social dynamics by itself. Though it may seem that theatre meanwhile got rid of this aspect of its social function, Girards idea seems still applicable if we simply replace the desire for any kind of objects by for example education as in the tradition of the "Bürgerliches Theater". But this description obviously has it limits when we think of all the inventions that have been made by artists in order to change theatre during the 20th century - they invented new artistic practices but did not change the institution in the end.
As I am not into sociologist system theory, I don't know how Niklas Luhmann or Dirk Baecker would (have) describe(d) the revolutions and catastrophies of the 20th century. What I know is that theatre in Nazi-Germany turned into a facist institution. I won't go deeper into this here. But I think if a serious of lectures is titled "Kritik der Institution" it's not enough to state that and how an institution is functioning. (Baecker goes as far as to say that there is not much possibility for change anyway only through exchange of staff in the organisation.)
In his book "Studien zur nächsten Gesellschaft" (Studies for the next Society) Dirk Baecker outlines where he sees the function of theatre in the computer era: theatre is helping the society to develop a culture of dealing with its problem of controlling the computer, "the Computer as a space of possibilties that we are exploring as much as it explores us."
"Das Theater nähert sich dem Computer, indem es die Adressen multipliziert, mit denen hinfort gerechnet werden muss. Handlung, Wille und Bewusstsein werden ergänzt durch Technik, Zufall und Prozess. Der Inbegriff für eine (solche) Technik (...) ist der Computer (...), ein Möglichkeitenraum, den wir ebenso sehr erforschen wie er uns." (Dirk Baecker: Studien zur nächsten Gesellschaft, S. 84, stw 1856, 2007)
If you follow the link you will also find a lecture by Bojana Kunst in English which I find very interesting and inspiring. She discusses how (small) institutions might be transformed through collective selfeducation. And how we need to slow down and take time for the complexity of the situation we are working and living in.