When the browser window is small enough, the website’s reactive design makes the playlist an overlay for smaller resolutions. When you trigger this change at around 1290px width and the playlist becomes an overlay, when you try to move playlist entries it no longer works. Dragging entries up/down does not change the playlist order, and requires you to resize the window to be larger in order to change the order.
Thanks a lot for this detailed bug report. The issue should now be fixed. Please give it a try!