The person uploading the video controls all of those pop-ups - how long they are, when they pop-up, and what they display. What if you were to create a video and use those pop-ups as choices for your students? Maybe there could be links to a webpage with more information. Maybe pop-ups that let students choose where to go as far as what they want to study? Maybe some sort of quiz where one video is the correct answer and the story continues, the other one is the wrong answer and a dead end? Maybe there could be links to collaboration webpages or documents.
I could see this as helping to differentiate a video. Students who need more help in math might click on a pop-up to get some review help before going on. An advanced student may click on something to move ahead. In a debate, maybe one pop-up could be one side of a question, the other pop-up the other side. You could almost design a whole set of instructional videos that branch off of one another and provide a bunch of resources and choices for students. The possibilities now look pretty good!
See where I'm going with this? These annoying click-me pop-up ads could actually be very useful to add some badly needed interactivity to videos.