Seeing as it's in continuity, and the Joker is alive and well, the whole "Batman killed him thing" is completely ridiculous and in no way possible. Batman laughed at the ridiculousness of the situation. The joke summed up their relationship, the art implies it even more (with the thin stream between their feet representing the gap from the joke), and Batman finally got the joke, and so he laughed.
Batman killing Joker after his entire speech about how it takes more than one bad day to mess someone up, and that there was just something wrong with the Joker to begin with would also be incredibly stupid. As would him promising Gordon that he would bring him in by the book, and then killing him in cold blood.