I don't believe that YouTube will let you play their hosted videos within a custom channel. You have to use one of their "players", available for a few platforms but not Roku. See https://developers.google.com/youtube/
for more information.
Alternatively, you may be able to accomplish what you need by other means, like hosting the videos elsewhere if you have the content. One more way would be to use the iOS or Android YouTube app to play the playlist, then screen share it with the Roku.