YouTube seems to be slowly rolling out a test of a new UI for minimized videos. Normally, minimizing a video will get you a small preview that takes up about one sixth of the screen sitting on the bottom while you navigate the app as you otherwise would. The new UI contains the video to a tiny preview window in the bottom left, which is at the far left side of a bar that contains playback controls. The bar can be scaled up and down, and the video scales up and down with it, allowing a user to decide how much of the screen they're willing to sacrifice for watching the clip in the preview window. After being brought up a certain distance, the bar transforms into a full-on YouTube window, some users report, adding that the new UI does not seem to contain any other noticeable changes.
This particular UI change has reportedly been in testing for a few months on various families of devices but is now starting to go out to a wider range of phones and Android versions. Reddit user "Therexin" who recorded the clip below, for instance, uses the Galaxy S8, but many users who are reporting having had this new UI for a while have Nexus and Pixel devices. Some people claim they had the same UI for a while, with others adding that it disappeared after a few weeks. Other users are reporting some bugs, such as having two bars, which were mostly resolved by uninstalling or resetting the app, then reinstalling it.
These changes do not seem to be rolling out in any particular order or with any particular timing, aside from Nexus and Pixel devices seemingly being among the first to get them. Google has not officially announced this kind of change for the YouTube app, but if the feature is in testing at this point, it's likely quite close to being ready for primetime, if Google does decide to roll it out to all users. Unannounced feature tests like this one tend to come and go at random, leading up to the feature in question either being passed on entirely, or rolled out to all users, so if you would like to try the functionality, keeping your YouTube app up to date seems to be one of the only ways to increase your chances of doing so.