I don't think the destination of the flight in question being HAM is relevant, since the decision to downgrade and acceptance thereof (by checking in and boarding the flight, even if not aware of the downgrade at the time) took place outside Germany.
Outside of EC261/2004 there is a term in German law which is called "Erfüllungsort" (location of fulfillment).
The highest German circuit court (one level below the supreme court) has decided in 2011 (BGH, Urteil vom 18.01.2011 – X ZR 71/10) that both the departure and arrival airport count as "Erfüllungsort", based on § 29 ZPO.
The downgrade happened on DXB-HAM. The court, in which district Hamburg airport lies, has jurisdiction in this case.
The passenger cannot refer to EC261/2004. That is for sure, however, the German civil code for the fulfillment of a transportation service applies.