The change only shows up when you're watching in full screen -- the app looks largely the same when you're watching a video in portrait mode. Doing so, however, used to come with the upside of having easy access to the share button and other controls. Now, you're getting that when watching in landscape view as well.
You're also now able to easily access the mode that lets you see comments alongside the video while in landscape. Before the new UI, you had to tap on the comment section while in portrait mode to open it up, then switch into full-screen mode. Now, you can pull them up by tapping the comment button.
The new UI is coming to both iOS and Android and started rolling out Monday, according to Google spokesperson Allison Toh. So far it doesn't appear to have made it to everyone.