The article overstates the case. I posted it because it's interesting, but the headline is hyperbole. It is the usual situation where an anomalous observation could lead to an important new discovery and a revolution in theory, but it may turn out to be an issue with the experimental setup, a confounding factor that no one has thought of, or some new phenomenon that can after all be accommodated without major theoretical upheavals.

Here's another source that reports that a Russian experiment has obtained results that fit with the Standard Model, so the discrepancy could be caused by any of these other factors, not by a deficiency in the Standard Model itself:

Dreams of new physics fade with latest muon magnetism result

(archive link)

So it's far too early to be saying we're on the brink of a scientific revolution due to these anomalous results. All we know is that the anomaly seems intermittent and is so far unexplained.