I guess if inbound flight is late and they can inform all passangers the only purpose of earlier checkin would be for an earlier depature if it's possible. I may be wrong but I recall BA is it, expect you to check in at original time but again could be wrong
I think it comes down to the station and it's interpretation of the rules. LHR when I have had a delay advised (rare) have sent a new text and while I can't remmeber the wording now, I believe it says your flight is due to depart at x, If I was to be challanged. I think I would simply show the text and show the EK website showing checkin at airport 90 mins before depature. Depature has been moved and therefore expect not to spend a day at the airport.
I guess the safe option would be to call EK and have them confirm, that way if they dispute, the station can argue with EK staff in Call Centre