I have only listened to the short clip available on the sky news site, but from what I have heard the pilot doesn't call a mayday or let the controller know that he is declaring an emergency and requires priority, I know he says he's hit birds and has lost thrust, but no emergency MAYDAY call.
Within 10 seconds of informing TRACON that he'd lost engines, TRACON informed LGA tower and had them stop all takeoffs so 1549 could return if able.
He may not have used the word mayday, but it seems clear that TRACON immediately treated it as an emergency.