I think he made a mistake. The term perichoresis like the term prosopon, comes from the world of the performing arts. If you think a little bit, you will realize that you have come across other words in English that use peri and choresis in some combination or in a simple alliteration. Peri is found as a prefix in words like perimeter, pericardium, peritonitis, etc. It means around, or surround.
Perimeter is the surrounding part of a given surface as in the perimeter of a triangle.
Pericardium is the tissue surrounding or enveloping the heart and peritonitis is something we better never get, the inflammation of the tissue surrounding parts of our digestive organs, as the appendix for example. Choresis is a term that you have heard many times inside nouns like choreography and choreographer and in the verb choreograph. It has to do with dancing. So perichoresis means to dance around. The three persons or roles of the Trinity act as One as they dance around.