You can always choose to not maximize the video, then it should be letterboxed.
The screen on the iPhone X is wider than a regular 16:9 screen, so full screen youtube content shouldn't be cut off, but rather be pillar boxed.
Like, right now, if you were to watch a video that is cinematic wide screen on your phone, there's letterboxed 16:9 and 'fill-screen', which already cuts off the sides of your video.
So, in 'fill-screen' mode, the iPhone still cuts off some of the image, but way less than the phones before it, while in regular viewing mode you'll have a (presumably less) letterboxed video.
I believe this to be the situation on the iPhone 6 with cinematic ratio video content:
and on the iPhone X it will be, i presume:
anything else would be rather absurd. So i'm guessing that's what we're getting. Less of a cut-off (yet with a weird, non-straight cut-off) when using fill screen. Less black bars when using full screen.