The fact that others (Starbucks,Amazon) seem to get away with paying a minuscule tax rate doesn't even begin make it a level playing field with the Middle East airlines. There's almost unlimited access to cheap (free?) capital. Labour costs which reflect medieval working practices (not hyperbole; In Qatar it is a criminal offence to leave your employment, even with wages unpaid for years) and finally, almost zero tax and social costs.
Regarding the amount of APD collected on EK flights, that argument only holds water if we assume aviation grinds to a halt if with a level playing field.