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"Sounds counter-intuitive to me.
You breathe out moisture and a mask would tend to help retain that."

The moisture you breath out is absorbed by the mask and dried out of the mask as you exhale.
The mask also absorbs the moisture in the air you are breathing in and again it drys out in the mask as the air moves through it.

If you go to the original source, you'll read :

" ... “Gum disease — or periodontal disease — will eventually lead to strokes and an increased risk of heart attacks,” says Dr. Marc Sclafani, another co-founder of One Manhattan Dental. He says the stinky syndrome is triggered by face coverings, since wearing a mask increases dryness of the mouth — and a buildup of bad bacteria. “People tend to breathe through their mouth instead of through their nose while wearing a mask,” says Sclafani. “The mouth breathing is causing the dry mouth, which leads to a decrease in saliva — and saliva is what fights the bacteria and cleanses your teeth.” He adds that “saliva is also what neutralizes acid in the mouth and helps prevent tooth decay and gum disease.” People’s tendency to drink less water while masked up, as well as consume more coffee and alcohol during lockdown, have also added to the widespread dehydration he’s seeing. On the bright side, the dentists say that they’re packing in breath-conscious patients who might otherwise neglect their dental health during the pandemic. “Patients are coming into us like, ‘Wow, my breath smells, I need a cleaning.’ [But] when you smell the bad breath, you either already have periodontal disease or you have a lot of bacteria that’s sitting on your tongue because of dry mouth,” says Sclafani. While masks are not negotiable given the times, Sclafani says there are things wearers can do to avoid their grossest side effect: drink more water, cut down on caffeine, snag a humidifier (to “help moisten the air”), use an alcohol-free mouthwash, scrape your tongue and don’t smoke. And If all else fails ? “Just breathe through your nose!” ... "