JFK are his initials, not a short form of his name. Illinois is, obviously, not the only state that voted for him. I've never heard of an airport being referred to as "an Institution", besides, there are several other entities in NYC that bear his name.
I've never stated that Illinois had been the only state voting for him or that the airport was the only thing named after him. But this quiz asks for a state starting with I that voted for him and for a place (how would you call it?) starting with A that is named after him.
But isn't Dallas a city?