Agreed. If a school does not ask for something such as a recommendation letter, then providing what is not asked for may hurt one’s chances. Sometimes Admission Officers will even state during the information session that the university of so and so does not accept reference letters so please do not send them. That some AO’s will state this sometimes due to the corresponding question posed by an audience member but often unprompted suggests not only that students have sent unrequested reference letters in the past but also that doing so is not viewed favorably.
Perhaps rather than look for a way to submit a video essay which was not requested and which does not seem to have a built in delivery system for the admissions committee to evaluate the content if they even wish to, you could look for schools wherein video essays are requested?