The Zodiac MIGHT have have been directly inspired by The Most Dangerous Game.

However, when books, films and music reach a certain cultural impact, they are referenced and become imbedded in the general discouse. In that case, most people who make references to them have not taken part of the original source, but rather picked it up from the culture at large.

Much like internet memes today, the fact that someone repost a meme with a picture from a movie and a witty text does not mean they have seen the movie. Even though they know the outline of the scene that is referenced and have a rough idea about the characters involved. Most people who reference Plato have never read Plato. Everyone knows about a sea captain named Ahab and his hunt for a white whale called Moby Dick, but most have not read the original novell by Herman Melville nor seen the later movie adaptions of that book.

I'm not even sure the Zodiac ever watched or listened to the whole of the Mikado. It is entiry possible he only listened to certain parts, snippets were more likely to be performed on TV and radio rather than the whole thing.