What are the original dimensions of the video and/or the dimensions in the course? It’s possible this is a Safari specific issue if the Chrome screen shot is from Chrome on the iPad. Testing with Chrome or Firefox on the iPad could help narrow down (or, worst case scenario, expand) the likely culprit(s).
My other initial thought is wonder if you are using responsive design and have a version for landscape tablet. Just some initial thoughts, as designing one site for both desktop and mobile has its perils.