"Fake" implies deception: it's fake because it counterfeits or forges something else that is real.
An anonymous or pseudonymous Twitter account run by a human, in the way that a human is expected to use a Twitter account, is not a fake account: it's real, just pseudonymous. A bot account that's clearly a bot, like @big_ben_clock or @choochoobot, isn't a fake account either: it doesn't pretend to be anything other than what it is.
From the article: "These accounts did not act like the bots other researchers had found but were clearly not being run by humans."
One thing a network of fake accounts could be doing is inflating follower counts. A follow from a pseudonymous account that corresponds to an actual human isn't fake. Even a constant factor or constant term from a small number of humans with multiple accounts isn't particularly deceptive. But thousands or millions of follows from accounts run by a handful of humans is deceptive.
Another thing a fake account could be doing is spreading propaganda by creating the impression that many people agree with a political opinion, when these "people" are just canned responses, or humans assisted by automation (but capable of making human replies across large numbers of accounts).