So we went to check out the exact location of the Al Mamzar ferry,  which was announced as a new route for the Dubai Ferry by the RTA in October 2014. The route was supposed to run every Thursday and Friday but as of now (November 2015), the route does not run at all due to lack of demand.

Instead you can take the water taxi or an abra ride from the Al Mamzar Marine Station which is located at Al Mamzar beach, just before the entrance to the Al Mamzar Beach Park.

It looks unlikely that the ferry will run from Al Mamzar at any time soon so you will need to take a trip from either the Marina or Al Ghubaiba at the present time.