There is a long thread on the eMed test in the Coronavirus forum. Issues re EMed/Abbot Binaxnow Navica Tests.

May be worth checking there if anyone has had a negative experience with EK accepting the test for travel to the U.S., but I don't think I've seen any instance of an airline rejecting it. EK flies lots of flights to the U.S. obviously, so they must have been presented with the eMed test quite a bit by now.

ETA: The language from EK does seem pretty clear. No idea why that's the policy.