Rights groups say the case is only the most recent example of the extreme sensitivity of Persian Gulf monarchies to the power of social media as a forum for critical — and uncontrollable — social and political discourse. Satire, especially of the political variety spread on social media, is treated as subversive. A number of Persian Gulf countries have laws against so-called cybercrimes, and in recent years a string of people have been jailed for content posted online.

But the case is also the latest instance of foreigners in Dubai — a city of extremes, with hard-partying clubs and conservative Emirati norms — getting entangled in the legal system for acts that might seem ordinary in the West, like public drinking or kissing.

In July, after a video showing an Emirati man hitting an Indian van driver spread rapidly, the police arrested the Emirati as well as the man who posted the video because he had “shared” images of a potential crime.

The case over the martial arts video is likely to embarrass the United Arab Emirates at a time when the country is advertising itself as an international destination for culture. Last week, Dubai won the bid to host the World Expo in 2020 under the slogan “Connecting Minds, Creating the Future,” after a lengthy campaign endorsed by Bill Gates.

Sheikh Mohammed bin Rashid al-Maktoum, the ruler of Dubai, said on Twitter that the Expo would “breathe new life into the ancient role of the Middle East as a melting pot for cultures and creativity.”