According to quite a few sources, it kind of is. It seems that the blanket Islamic laws of the UAE do not entirely apply to Dubai in an attempt to merge Islamic law with more modern laws so as to be more friendly to international business.

"When advising clients, I always inform them that UAE courts will pass judgment according to Sharia in the absence of a provision of UAE law covering the issue on which they are in front of the courts."1

Dubai and Ras al Khaimah are the only emirates that do not conform to the federal judicial system of the United Arab Emirates. The emirate's judicial courts comprise the Court of First Instance, the Court of Appeal, and the Court of Cassation. The Court of First Instance consists of the Civil court, which hears all civil claims; the Criminal Court, which hears claims originating from police complaints; and Sharia Court, which is responsible for matters between Muslims. Non-Muslims do not appear before the Sharia Court.2

Non-Muslims are required to respect Sharia law in Dubai and conduct themselves accordingly.3

Do you have anything that says otherwise? This was just my understanding.

**EDIT - I also confirmed with a friend who works for an option trading house in London who has spent time in Dubai that yes, they are under Sharia law.