This is a bit different than the original though, since the time travel of Cornelius effected the outcome of the future.
Let's not forget that we haven't seen yet all the events leading up to the situation. In the old films, all the dogs had died off due to some viral dealio, and humans turned to apes and chimps as companions. That meant there were millions of them, a much bigger threat if intelligent than they'd be in our current situation. Think if all the dogs and cats on the planet got smart enough to rebel and had opposable thumbs. That monkey that can fashion a pick to unlock things sure as hell can point a gun and pull a trigger.
But in the originals, there was also the time travel paradox - although the apes were smart enough to do basic chores and communicate, it wasn't until Cornelius returned with Caesar that they had a leader that could create the revolution. Not sure how they plan on handling that, but it looks like he's just a super smart chimp created by the drug, which takes away a bit of the cool time travel feature of the original series.
I'm also cautiously optimistic. I can handle the idea of Caesar being a super chimp rather than a time traveler, but they are going to have to create a solid sci-fi backstory as to why there are so many apes that they can actually take over the world.