Due to the limitations of Responsive Slides, Auto Play is automatically disabled when you add a video to a slideshow.
Responsive Slides is a very small slideshow library, but it doesn't offer us a way to pause the slideshow once a video starts playing. Due to this, auto play is disabled automatically when a video is present in the slideshow. This ensures the slideshow doesn't move to the next slide while a video is playing.
Flex Slider on the other hand does allow us to pause the slideshow while the video plays, then resume the slideshow when the video stops. Therefore, the solution is to switch to Flex Slider.