Of course they're taking over. We are provoking a massive extinction of species in the oceans. Jellyfish are the one group of species we have no use for, so they're taking the free space we give them while enjoying the disappearing of their predators.
I didn't read the article but I saw a documentary on the subject. It said that they take over because the reproduce like rabbits, can live everywhere (in the sea), and kill anything they come across. It's not something we caused, or at least there isn't evidence about that.
Hm, and after some hundreds of thousands of years to have the opportunity to do this, jellyfish randomly decide to start doing this in the 20th century?
The article cited two primary causes of the population explosion: the destruction of sardine populations from over fishing (sardines compete with jellyfish for the same food sources), and expansion of eutrophic zones due to agricultural run off (fertilizers).
Not to forget the ocean acidification from CO2 emissions, which kills important ecosystems like coral reefs, while seemingly being harmless for jellyfish.
Populations in nearly every ecosystem have shifted in response to human introductions of formerly isolated species from other regions. The change really is dramatic - in the last two hundred years the northeastern US forests, which I've studied somewhat, have completely lost the dominant overstory plant, the American Chestnut (introduced fungi), and have lost a many-inches-thick layer of topsoil debris with resident moss & fungus populations (introduced earthworms). That's in the ones that have recovered from the agricultural/logging clearcuts and that weren't affected by the fire suppression.