A Reddit user by the username fmarx1 spotted a new feature in the non-beta MyTube Universal Windows App allowing you to continue watching your current video on other Windows 10 devices with the app installed. The feature is using the new "continue app experiences" API that allows developers of apps like Readit to let you continue doing whatever you were doing on one device and transfer it to other devices by simply pressing a button.
A screenshot of the feature, provided by the abovementioned user, can be seen below:
All you have to do to get the feature up and running is to download MyTube on both (or more) devices you are planning to use it on, press share, then select devices, and you're almost done. Now select the device you want to watch the video on and viola.
You can go ahead and download the YouTube client below. Let us know in the comments what you think about this new functionality.