Predicting positive/negative experience with very few labels and labels from only one class
This is not a data science solution, but wouldn't the fact that the user watched the video in the first place (took the time to find and locate the video then started the video) imply that the user have some interest in that particular video over users that never interacted with the video? I would consider the fact that the entry exists as a positive response, the lack of a "like" as a neutral response, and (maybe?) the lack of watching it as a negative response. It, of course, depends heavily on the source and assumptions of your dataset.

Nonetheless, I agree that clustering the videos with likes is a good starting point in this situation, and that would definitely be my first gut instinct thing to do.