Its called a gun, you shoot chimp its dead. It doesn't matter if it has got the smarts.
That works if you have a loaded gun on you all the time and don't mind murdering chimps who may or may not want to harm you.
I don't think it's absurd that super intelligent apes would overthrow us, the fact you find it absurd is a card in their favor. Imagine calling in backup because a bunch of gorillas are shooting at you. The time spent scrambling from just how bizarre the whole deal is could be enough time to get some more apes to increase your ranks. That's the problem I have, though, is that there cannot be enough apes to kill or capture six billion humans. Each ape would need to kill like a million people, which is insane. Plus, most apes are only found in Africa so they'd have to organize there and then make their push. I'm assuming in this movie they experiment with apes in a first world country, which would require that ape to either flee to Africa or call in his buddies - which, if their intelligence is due to a drug, would mean he couldn't perform the latter.
I guess I'll have to watch the movie.