Earlier quoted context omitted.
The "nonsense news headline" and followup discussion are less critiquing MWI than poking fun at David Deutsch. This is because Deutsch is a prominent critic of PWT. The arguments against MWI from Occam's Razor are indeed weak. The stronger critiques are the difficulty of deriving the Born rule, or indeed quantum randomness at all, from the deterministic MWI. This is presumably what the authors hint at in their "doubt…
Why do you say that quantum randomness is a problem in MWI? I thought it was one of the neat things of MWI that it doesn't require randomness. There are no random events: instead you have a branch for each outcome. The only randomness is which branch you find yourself in as an individual.
So if it's right, it needs to rigourously exclude everything else.