Emacsen are editors. Not just any editors. They are editors fully programmable, usually with a look-and-feel similar to EmacsAndXEmacs. An Emacs programmable in Haskell or Python is still an Emacs, one of emacsen. A Vi programmable in Lisp is not an Emacs, unless you can switch from the Vi-like look-and-feel to an emacsen look-and-feel.
What is a programmable editor? It allows you to edit text files. And since you can program it, eventually you can also write mail, edit HTML, read news, and highlight your source. And more. Much more.
“Emacsen” is offered as a plural to Emacs in the Collins English Dictionary, and gives “Emacs” the definition of:
See the excellent list of EmacsImplementations for more information.