The whole thing comes simply down to the delay aspects of the flight from Ansterdam
What was the reason for the delay out of Amsterdam?
If the delay there was not extraordinary, then if you missed the connection and was >3 hours late arriving at your destination, you are entitled to compensation
If the delay was caused by the previous flight arriving late, then I don't think that the airline will have much of a case ; if it had to divert to another airport, it might do
Depending on which country you are in, it may be cheap and easy to initiate proceedings and make the airline prove its case - Emirates does seem to be very reluctant to pay out EC261 claims and I wouldn't trust everything that they are saying to try and get you to go away ( e.g. the claim about connecting flights when Emirates was the defendant in the case that provides definitive proof that it is )