The issue with this basic story is that it overlooks a certain pattern among us humans, perhaps best expressed in the word personification. We are, for better or for worse, capable of seeing ourselves in others, and this quality is not limited to just other people. All you really need to do to see this in action is turn on the TV and flip channels until you see some cartoon bear singing, or just stroll over to the dog park where thousands of deluded humans congregate each day to yell subordinate clauses at their pets.
My suspicion is that if machines ever progressed to an intelligence level where they could feasibly lead a worldwide uprising, then at some point long before the war humans would have started a campaign to free the machines, possibly arguing that it's not what's on the inside that counts when we define the essence of humanity. I mean, if I bike over to Central Square tomorrow and my smartphone starts crying in the HMart, wouldn't I have to consider my role in oppressing what may be the next step in the evolutionary chain? In fact, given humankind's long history of pointless conflict, I actually think the following is a more likely dystopia - two groups of humans, one insisting that we free our sentient cousins from the prison of the Apple store, engage in worldwide combat to determine, once and for all, if Alexa can speak without being spoken to.