The issue is that an iframe and video can't scale like an image, where it gets the proportionally correct height based on the aspect ratio if you just leave the height at the default.
A solution for this is to figure out the native width/height of your video, and do a little math to figure out what the height should be at 100% screen width. Assuming it's 1920x1080, you can do something like this using viewport width (vw). You can reduce the 100vw to whatever fits better, if you don't want it to literally fill the screen.
iframe{
width: 100vw
height: calc(100vw/1.77);
}
