IME over the past years, KE has always had an amenity kit in coach for the JFK - ICN route. The contents have varied over time-- Ive see the 'footwear' go from slippers to socks to paper slippers over the years....
I noticed to OP said that it was a family receiving an amenity kit; KE has a special children's amenity kit that Ive seen on the route I fly... maybe thats what it was?