Based on what I've seen of the script reviews, this sort of does it. I believe it focuses some on animal experimentation and genetic engineering. It also ties into the original film, the mission Taylor is on is mentioned during a news report.
Also I have read the book. The ending is close to that of Burton's film, except for the city the character lands in. The main plot is basically the same as the movie minus the action and the twist. Actually worth checking out if you can find it.
Read the Pierre Boulle book millions of years ago, seems like it anyways.
I think Serling's input into the screenplay made the first film resonate such that it made the viewer look into a mirror of humanity, it exemplifies the power of good science fiction.
I don't think a direct version of the book could have done that as well, but it's been so long since I read it apes could have evolved intelligence since then. So my memory is very fuzzy on the source material.