Youtube videos are wider than they are high (16X9 ratio of width to height), so you can't show them full screen on a screen that's higher than it is wide. It has nothing to do with the phone, it's mathematically impossible unless you stretch the picture out vertically. Then you get tall, thin people.
When you hold the phone vertically, the picture takes up the full width of the screen, so it's shorter than the length. They could expand it to full screen, but they'd have to chop it off at the sides, so you'd see only about 1/3 of the picture horizontally.