Technically the DL flight in and of itself wouldn't normally qualify.

However as this was bought as one ticket from KLM, KLM is on the hook. (This is because of court rulings) DL can Technically also be pursued for payment and they can go after KLM to be paid back.

When it comes to flights outside/not departing from EU, the rules for non-EU carrier operated, but EU carrier marketed flights get complex.

I recommend filing with a company like click2refund or similar. (Only mention them as I've used them in the past)

When it comes to EC261, nowadays I attribute non-payment to complexity court rulings have caused. What was a fairly straightforward rule has become so complex even a lawyer will have problems following the nuances.