An additional note: This is a TV timeline. A lot of dates in Planet of the Apes are given in the movies, so it doesn't so up in this version. The Logan's Run tv show and film offer different starting dates, but the show is being used here (though in my game, should the City of Domes ever show up, I'm using the movie date).
Creation of cyborgs (like the Six Million Dollar Man) may also rank among the late 20th Century's achievements.
Suspended animation was used in spaceflight in the 80s, so either a less developed version was already in use (as suggested by the POTA films) or data from Hunt's project did lead to a breakthrough despite the loss of the team leader.
The actual date is August 19, 1980.
This is also true of the 2nd Roddenbery pilot to deal with this material, Planet Earth. There Dylan Hunt is played by John Saxon.
No evolved apes are seen at the time of PAX (or even Logan's Run), true, but it could be the apes were confined to the area that once was California then. Neither of these shows necessarily covered a wide territory.
Astronauts Burke and Virdon arrive in a North America (or at least Western North America) controlled by apes in a well-established civilization in 3085, so the culture must have spread before that.