At Amsterdam’s Schiphol airport, that announcement goes approximately like “WOULD MR JOHN DOE BOOKED ON KLM 123 TO LONDON HEATHROW PLEASE PROCEED TO GATE A123 IMMEDIATELY. YOU ARE HOLDING UP THE FLIGHT!!!”
Incidentally that is an obvious argument in favour of checking baggage. If you’re travelling with cabin baggage only, then if you’re not there when the gate closes, they don’t have to search the hold of the aircraft for your stuff and can more easily leave without you.
