No, a magnetic reversal does NOT happen around once every 13,000 years. Their interval, in fact, is highly irregular, perhaps even chaotic. The last major reversal was 780,000 years ago, although there were temporary collapses in magnetism since then, which I presume is what this article is calling a reversal. Some reversals were millions of years ago, some happened within several thousand years of each other, if you count these momentary collapses as reversals.
The magnetic field is currently weakening; this in no way suggests a major or minor reversal is coming. At the current rate of collapse, it would take over 1000 years to completely collapse, and such variations are completely normal outside of any long-scale trend.