>...where are the apes?
No apes. But there is a cathederal with a nuclear bomb in it.
There are mutant humans in it and primitive humans. I think they used Kim Hunter as a template for tribal women. Also, check out the colours of the buildings, countryside and the clothes on the tamed humans. Tamed humans are in a later POA movie set 10 years later. I think it was called Return to the Planet of the Apes.
There several distinct races with their own belief systems, agendas and histories. Not bad for 1970. Were role playing games even around back then?
The movie has the Forbidden Zone, which is a radioactive desert/wasteland. There is a brief shot of a nuked city that reminds me of the main screen in Fallout. The mutant humans live under the city and worship a dooms day bomb.
So I'm not saying the Fallout creators copied POA, but I do think it was a major influence. Of course Mad Max was another influence, but everyone knows about that, so I didn't mention it.
Anyway if you haven't seen it, do yourself a favour and check it out.

I think 7 POA movies were made.