In order to play downloaded videos, you need to use an external video player.

The team has considered implementing this directly into NewPipe. This idea was dropped due to the following reasons:

• A phone is usually shipped with a video player.
• There are other apps available that deal with offline playback, in case the phone doesn't have one.
• One option that could reduce friction between using NewPipe and an external player is Just Video Player, available on F-Droid, which is also based on ExoPlayer like NewPipe's player.
• NewPipe is not designed to be an all-around video player.
• A huge additional maintenance effort would be required to make this work.