Chris

To the original question: any decent router has logs of the urls it has served up. Whether Starbucks staff can access it will depend on how internet service is provided to customers. I suspect that they probably can't.

Content filtering is normally performed at the domain name level. Filtering services don't normally try to identify and block specific content within otherwise approved websites (like YouTube).

Finally, there are any number of reasons for a customer to choose their seat, use headphones and even to view gymnastics videos. Such behaviour isn't illegal even if in his heart of hearts he is a complete pervert. Unless you see him doing something that really is criminal, you risk embarrassing everyone concerned by expressing your discomfort.