I find it interesting that, in contrast to the other things that the article mentions that techniques like this can be used to predict ("We can try this on traffic data to predict the duration of a bus ride, on movie ticket sales, on stock prices, or any other time-varying measurements."), Twitter trends are artificial phenomena, with a very precise definition that was created by Twitter, not some natural emerging thing. The actual tweets are of course a natural phenomenon, but how topics are selected from them as 'trending' is not.
Of course, that's not to say this is not impressive work - predicting what Twitter's proprietary algorithm will select as trending without direct knowledge of the algorithm, before it selects them, and before all the tweets that make them be selected are made is impressive, and no doubt not any easier than predicting more natural phenomena or emergent behaviours.
You bring up a great point. To classify something as a trend or not a trend, we have to use this artificial black box to supply ourselves with examples of what's a trend and what isn't. The nice thing, IMO (and this is something I admittedly gloss over at the very end) is that doing prediction/forecasting with this method is almost the same as doing classification, even though you don't have any labeled examples when doing prediction. To do classification, we compare current activity to past examples of activity, and decide if it looks like the positive examples or the negative examples. For prediction, we compare current activity to past activity, and see how similar-looking past activity continued to evolve over time.
Of course, that's not to say this is not impressive work - predicting what Twitter's proprietary algorithm will select as trending without direct knowledge of the algorithm, before it selects them, and before all the tweets that make them be selected are made is impressive, and no doubt not any easier than predicting more natural phenomena or emergent behaviours.