Elections are won or lost at the margins. Given that Hillary Clinton was in favor of having the government fund any and every gruesome late-term abortion technique, probably including dropping living babies into Cuisinarts as they were delivered, there was no way on Earth I was going to vote for Ms. Abbatoir. If Instapundit ran a story telling me that Hillary was Elvis' love child and I swallowed it hook, line and sinker, it would have made no difference.
Similarly, if the Huffington Post had run story after story telling me that ObamaCare was going to lower costs and provide awesome coverage, I wouldn't have ... oh, wait. They did.
In any case, the HufPo didn't change my opinion at all.
Most of us live in intellectual bubbles, reading stories and columns from people and sites that agree with us. The actual impact of "fake news" stories is probably pretty minimal as they just reinforce opinions that are already set in concrete. The only way a "fake news" story could effect things would be if they appeared on sites who hold positions contrary to the point of the story.
If HuffPo carried the Elvis-Hillary story or Glenn Reynolds told me ObamaCare was fantabulous, it would at least have a prayer of making an effect. As it was, I can't see how any "fake news" stories did anything at all to impact the election.
Another mechanism would be to have the thin sliver of undecideds exposed to sufficient amounts of "fake news" to change their minds. How this would differ from the major news networks going all-in to stop Trump, I'm sure I don't know.