So when I play a video, that means the video is moved from backing store to main memory. Then if I remove my laptop's battery all of sudden, that means the video should get lost as main memory is volatile. Why doesn't this happen though?
Because it isn't moved: it's copied.
Main memory is volatile, secondary memory is not. The video is physically stored in the secondary memory(hard drive). The main memory just fetches this data and copies it in a location on command by the program making the fetch. (video player for this example) This data is lost from the main memory since it requires constant "refreshes"(power) to access temporally stored data in it. Therefore if you remove the battery the main memory loses it but the secondary memory doesn't since it doesn't require a constant "refreshes", its magnetically saved and doesn't depend on a power source to stay there.