I guess it’s effective and memorable because even months later, I remember the gist of the accuracy claim (though not the hardware item name)
Here is an article from 2020 from MIT using the same units and wording: https://news.mit.edu/2020/passive-solar-powered-water-desali...
I do agree its confusing.
edit: Later in the MIT article they state their device (which is also a 5.8L/m2 system) - "[...] roughly 1-square-meter solar collecting area could meet the daily drinking water needs of one person.
So I will assume the numbers are per day.
edit2: On second thought, the units aren't that confusing. We already use "BTU", for example, to measure air conditioner performance. We just know that means "per hour". Then just the additional complexity of it being based off surface area. "We bought a 6L/m2 solar desalination plant" sounds the same as "We bought a 15,000 BTU A/C unit". Consumer marketing would drop the sizing - "We just bought a 10L desalination plant" and the thing is as big as it needs to be.