[Vuejs]-Can't call child window functions

First, from the window.open() documentation:

windowName

… The name should not contain whitespace. …

Return value:

A Window object representing to the newly created window.

Your this.presentation contains Window object, not the Vue object. Of course, it doesn’t have setPage() method.

Perhaps, something like that could work (in your child component):

{
  mounted() {
    window.setPage = (page) => this.setPage(page);
  }
}