Move saved YouTube videos between devices

I am afraid to say this but moving videos between devices is not supported, Yet, AFAIK.

Here are few technical details.

When user download those videos, using official YouTube app, Android saves those videos on Internal storage(and not on external store such as sd-card)of the device. The path can be something like below:

Internal
storage/Android/data/com.google.android.youtube/files/Offline/(system
generated folder name)/streams

If you can go to that location, you will find that, all those downloaded files are saved as .exo files.

Since these .exo files are supposed to be system files, these are usually filled with System info(in another words, the device info) into it. Also, those downloaded videos are encrypted and the video file is split into chunks of .exo files.

Hence not only they can be played on the same device, but they can only be played with Official YouTube app.

You can not play these downloaded videos using any Other Media player.

You may want to check the links related to YouTube offline feature here and here for more information.