"sum of the emfs located on the path". In order to know that the induction emf is 'distributed' along the path and in what manner you need fields. And that was not common knowledge at the time Kirchhoff wrote this paper. I analyze what Kirchhoff wrote, not what he could have meant knowing the corpus of knowledge developed after that time.

I based my answer on what Kirchhoff had written at the time, based on what he had used at the time. I believe that from the point of view of an historian it is better to avoid speculations about what Kirchhoff could have thought had he known what we know today, or even four or eigth years later. See the comment in your original question.