Seems like there is confusion about flame out actions even when not in the air with the emergency happening around you. Appreciate this is a -500 not -600 but assume not much difference. Can only assume the engine problem, presence of 3rd person in cockpit, pre-knowledge of faulty engine and emergency happening in a densely populated area may have been information overload for the crew.
Standard departure seems to be a right hand turn and from the flightpath graphics, it started but then deviated from that and commenced a left hand turn before turning right again to its final position. Could the pilot have been attempting to return to the airport but on seeing they were unlikely to make it, aimed for the open space of the river?
http://www.pprune.org/tech-log/44625...-take-off.html